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Sidorov, Nikolai Aleksandrovich

Total publications: 134 (128)
in MathSciNet: 99 (99)
in zbMATH: 60 (60)
in Web of Science: 36 (35)
in Scopus: 17 (16)
Cited articles: 80
Citations in Math-Net.Ru: 250
Citations in Web of Science: 150
Citations in Scopus: 73

Number of views:
This page:4307
Abstract pages:11160
Full texts:4520
References:795
Sidorov, Nikolai Aleksandrovich
Professor
Doctor of physico-mathematical sciences (1983)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: ,
Keywords: branching theory of nonlinear equations; bifurcation; singular problems; rgularization; approximate methods; differential-operator equations; kinetic systems
UDC: 512.547, 513.8, 513.881, 514.958, 517.432, 517.93, 517.948, 517.958, 517.988.67, 518.5, 948, 517.95, 517.91, 517.98, 519.21, 519.53, 517.988.7
MSC: 47H17, 65H17, 58F14, 47H15, 47A55, 47A75, 58E07, 45G10

Subject:

Principal investigation concerns the theory of branching solutions of nonlinear equations. The general existence theorems for bifurcation points, curves and surfaces are proved by consideration of the branching equation reduced to the canonical form with the use of combinations of analytical, topological and algebraic methods. The proof method for these theorems intensively uses the Jordan structure of a linearized problem, as well as application of the Kronecker - Poincare Index, the Morse - Conley Index and search of conditional extremum points of the definite functions corresponding to the branching equation. The method is also aplicable in the case of a vector parameter when the bifurcation points of a solution can fill in curves or surfaces. It makes it possible to construct an asymptotics of appropriate solution branches and consider their stability. The general theory is used for a problem of branching solutions of nonlinear elliptic equations classes and applications (e.g. the existence theorems are proved and the asymptotics of solutions of the Karman boundary value problem for systems with a biharmonic operator is constructed, the solutions of integral compensation equation of the theory of superconductivity are constructed, the bifurcation analysis of some problems for kinetic Vlasov-Maxwell systems which describe a behaviour of multicomponent plasma is realized.) The analysis of generating of free parameters in branching solutions of general classes of the nonlinear equations in Banach spaces is carried out on the base of the interlaced branching equations theory, constructed for this purpose. The backgrounds of the theory of iterative methods in a neighborhood of solution branch points of the nonlinear equations in Banach spaces are developed: the method of sequence of successive approximations with an explicit and implicit parametrization of branches, including most general N-stepped iterative method with the explicit indication of uniformization of branching solutions and construction of an initial approximation are offered; the methods of a regularization of calculations in a neighborhood of solution branch points ensuring uniform approximation of branching solutions are given. The basic results in the theory of differential - operator equations (ordinary and in partial derivatives) in Banach spaces with an irreversible operator in the main part are obtained: the existence theorems in linear and nonlinear cases are proved; the methods of reduction of this problem to the ordinary differential equations of the infinite order, to "scalar" integral equations, to the differential equations with a singular point are offered; the method of construction of classic and generalized solutions on the base of a Jordan structure of operator coefficients of a linearized equation is developed. More than 100 articles were published and reviewed (see some abstracts of these articles in Mathematical Review : 87a:58036; 98f:47069; 98d:35221; 96k:65042; 95c:47079; 93m:82047; 93a:47054; 92i:47077; 90m:58033; 89i:45018; 85j:34139; 85b:34072; 82a:47011 etc.)

Biography

Honored Scientist of the Russian Federation.

Graduated from Faculty of Physics and Mathematics Irkutsk State University (ISU) in 1962. Ph.D. thesis was defended in 1967. D.Sc. thesis was defended in 1983.

In 1999 was awarded the sign " Honorable member of Higher Professional Education in Russia". Academician of Academy Sciences of Nonlinear Sciences -1998, Member-Correspondent of Academy Sciences of Higher School of Russia-1999.

   
Main publications:
  • N. Sidorov, D. Sidorov, A. Sinitsyn, Toward General Theory of Differential-Operator and Kinetic Models, World Scientific Series on Nonlinear Science Series A, 97, eds. Leon O Chua (University of California at Berkeley, USA), World Scientific Series, Singapore, 2020 , 496 pp
  • Nikolay Sidorov, Boris Loginov, et al Lyapunov-Schmidt methods in nonlinear analysis and applications, Mathematics and its Applications, 550, Kluwer Academic Publishers, Dordrecht, 2002

http://www.mathnet.ru/eng/person11024
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:sidorov.nikolai-aleksandrovich
https://mathscinet.ams.org/mathscinet/MRAuthorID/195498
http://orcid.org/0000-0001-9331-1921
https://publons.com/researcher/552109/nikolai-a-sidorov/
http://www.researcherid.com/rid/K-9743-2013
https://www.scopus.com/authid/detail.url?authorId=57197851137
https://www.researchgate.net/profile/Nikolai_Sidorov

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |



   2021
1. S. Noeiaghdam, D. Sidorov, A.-M. Wazwaz, N. Sidorov, V. Sizikov, “The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method”, Mathematics, 9:3 (2021), 260 , 15 pp.  crossref  isi  scopus
2. A. S. Andreev, I. V. Boykov, P. A. Vel'misov, V. Z. Grines, E. V. Desyaev, D. K. Egorova, R. V. Zhalnin, E. B. Kuznetsov, I. V. Lutoshkin, A. G. Lvov, T. Ph. Mamedova, S. M. Muryumin, I. P. Ryazantseva, P. V. Senin, D. N. Sidorov, N. A. Sidorov, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “To the 80th anniversary of Vladimir Konstantinovich Gorbunov”, Zhurnal SVMO, 23:2 (2021), 207–210  mathnet  crossref

   2020
3. S. Noeiaghdam, A. Dreglea, J. He, Z. Avazzadeh, M. Suleman, M.A.F. Araghi, D.N. Sidorov, N.A. Sidorov,, “Error estimation of the homotopy perturbation method to solve second kind Volterra integral equations with piecewise smooth kernels: Application of the CADNA library”, Symmetry, 12:10 (2020), 1730 , 16 pp.  crossref  scopus (cited: 24)
4. N. Sidorov, D. Sidorov, A. Dreglea, “Solvability and bifurcation of solutions of nonlinear equations with Fredholm operator”, Symmetry, 12:6, 920 (2020), 1–21  crossref  scopus
5. E.M. Rojas, N.A. Sidorov, A.V. Sinitsyn, “A boundary value problem for noninsulated magnetic regime in a vacuum diode”, Symmetry, 12:4 (2020), 617 , 14 pp.  crossref  scopus
6. S. Noeiaghdam, D. Sidorov, V. Sizikov, N. Sidorov, “Control of accuracy on Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method”, Applied and Computational Mathematics, 19:1 (2020), 87–105 link, arXiv: 1811.09802
7. N. Sidorov, D. Sidorov, A. Sinitsyn, Toward General Theory of Differential-Operator and Kinetic Models, World Scientific Series on Nonlinear Science Series A, 97, eds. Leon O Chua (University of California at Berkeley, USA), World Scientific Series, Singapore, 2020 , 496 pp.  crossref
8. N. A. Sidorov, “The role of a priori estimates in the method of non-local continuation of solution by parameter”, The Bulletin of Irkutsk State University. Series Mathematics, 34 (2020), 67–76  mathnet  crossref  isi  scopus
9. N. A. Sidorov, A. I. Dreglea, “Differential equations in Banach spaces with an irreversible operator in the principal part and nonclassical initial conditions”, Differential Equations and Optimal Control, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 183, VINITI, Moscow, 2020, 120–129  mathnet  crossref
10. N. A. Sidorov, D. N. Sidorov, A. V. Sinitsyn, “Review of monograph “Toward General Theory of Differential-Operator and Kinetic Models””, The Bulletin of Irkutsk State University. Series Mathematics, 32 (2020), 118–123  mathnet  crossref  isi  scopus

   2019
11. N. A. Sidorov, “Classic solutions of boundary value problems for partial differential equations with operator of finite index in the main part of equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 55–70  mathnet (cited: 1)  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 2)
12. N. Sidorov, D. Sidorov, Y. Li, “Basins of Attraction and Stability of Nonlinear Systems Equilibrium Points”, Differential Equations and Dynamical Systems (Springer), 2019, 09713514 , 14 pp.  crossref  zmath  isi (cited: 1)  scopus (cited: 3)
13. N. Sidorov, D. Sidorov, Y. Li, “Nonlinear systems equilibrium points: branching, blow-up and stability”, All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019 (Technopark of Novosibirsk Akademgorodok, Novosibirsk; Russian Federation; 13 May 2019 through 17 May 2019;), Journal of Physics: Conference Series, 1268:1 (2019), 012065 , 6 pp.  crossref  isi (cited: 3)  scopus (cited: 3)

   2018
14. N. A. Sidorov, D. N. Sidorov, Yong Li, “Areas of attraction of equilibrium points of nonlinear systems: stability, branching and blow-up of solutions”, IIGU Ser. Matematika, 23 (2018), 46–63  mathnet  crossref  isi
15. A. I. Dreglea, N. A. Sidorov, “Integral equations in identification of external force and heat source density dynamics”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 3, 68–77  mathnet (cited: 2)  mathscinet  zmath
16. N. A. Sidorov, O. A. Romanova, M. V. Falaleev, D. N. Sidorov, V. K. Gorbunov, A. I. Dreglea, “In the memory of professor Boris Vladimirovich Loginov”, IIGU Ser. Matematika, 23 (2018), 96–99  mathnet

   2017
17. A. I. Dreglea, N. A. Sidorov, “The identification of external force dynamics in the modeling of vibration”, IIGU Ser. Matematika, 19 (2017), 105–112  mathnet  crossref  isi
18. D. N. Sidorov, N. A. Sidorov, “Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:2 (2017), 63–73  mathnet (cited: 6)  crossref  isi (cited: 9)  elib
19. N. A. Sidorov, D. N. Sidorov, “Skeleton decomposition of linear operators in the theory of nonregular systems of partial differential equations”, IIGU Ser. Matematika, 20 (2017), 75–95  mathnet  crossref  isi

   2016
20. Leonardo Rendón, Alexandre V. Sinitsyn, Nikolai A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov-Maxwell system”, Rev. Colombiana Mat., 50:1 (2016), 85–107  crossref  mathscinet  zmath  scopus (cited: 2)
21. I. R. Muftahov, D. N. Sidorov, N. A. Sidorov, “Lavrentiev regularization of integral equations of the first kind in the space of continuous functions”, IIGU Ser. Matematika, 15 (2016), 62–77  mathnet

   2015
22. N. A. Sidorov, D. N. Sidorov, I. R. Muftahov, “Perturbation theory and the Banach–Steinhaus theorem for regularization of the linear equations of the first kind”, IIGU Ser. Matematika, 14 (2015), 82–99  mathnet
23. O. A. Romanova, N. A. Sidorov, “On the construction of the trajectory of a dynamical system with initial data on the hyperplanes”, IIGU Ser. Matematika, 12 (2015), 93–105  mathnet
24. I. R. Muftahov, D. N. Sidorov, N. A. Sidorov, “On perturbation method for the first kind equations: regularization and application”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:2 (2015), 69–80  mathnet (cited: 1)  crossref  isi (cited: 2)  elib
25. N. A. Sidorov, “The chronicle of the Irkutsk regional branch of research-methodological Council on mathematics of the Ministry of Education and Science of the Russian Federation”, IIGU Ser. Matematika, 11 (2015), 106–107  mathnet

   2014
26. N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Math. Notes, 96:5 (2014), 811–826  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 14)  elib  elib  scopus (cited: 12)

   2013
27. N. A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system”, Izv. Irkutskogo gos. un-ta. Ser. Matematika, 6:4 (2013), 85–106  mathnet
28. N. A. Sidorov, M. V. Falaleev, “In the memory of Trenogin Vladilen Aleksandrovich”, IIGU Ser. Matematika, 6:4 (2013), 138–140  mathnet

   2012
29. N. A. Sidorov, R. Yu. Leontiev, A. I. Dreglea, “On Small Solutions of Nonlinear Equations with Vector Parameter in Sectorial Neighborhoods”, Math. Notes, 91:1 (2012), 90–104  mathnet  crossref  crossref  mathscinet  isi (cited: 8)  elib  elib  scopus (cited: 8)
30. N. A. Sidorov, D. N. Sidorov, R. Yu. Leont'ev, “Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case”, J. Appl. Industr. Math., 6:3 (2012), 387–392  mathnet  crossref  mathscinet  elib
31. Denis N. Sidorov, Nikolai A. Sidorov, “Convex majorants method in the theory of nonlinear Volterra equations”, Banach J. Math. Anal., 6:1 (2012), 1–10  crossref  mathscinet  zmath  isi (cited: 15)
32. N. A. Sidorov, D. N. Sidorov, “On successive approximations of solutions of a singular Cauchy problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 238–244  mathnet  elib
33. N. A. Sidorov, M. V. Falaleev, “Continuous and generalized solutions of singular integro-differential equations in Banach spaces”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 62–74  mathnet

   2011
34. N. A. Sidorov, D. N. Sidorov, “Small solutions of nonlinear differential equations near branching points”, Russian Math. (Iz. VUZ), 55:5 (2011), 43–50  mathnet  crossref  mathscinet  scopus (cited: 4)
35. D. N. Sidorov, N. A. Sidorov, “Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials”, Autom. Remote Control, 72:6 (2011), 1258–1263  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  elib  elib  scopus (cited: 3)
36. R. Y. Leontyev, N. A. Sidorov, “An uniformization and successive approximation of solutions of nonlinear equations with vector parameter”, IIGU Ser. Matematika, 4:3 (2011), 116–123  mathnet
37. D. N. Sidorov, N. A. Sidorov, “Method of monotone majorants of the theory of nonlinear Volterra equations”, IIGU Ser. Matematika, 4:1 (2011), 97–108  mathnet
38. N. A. Sidorov, M. V. Falaleev, O. A. Romanova, “Vladilen Aleksandrovich Trenogin”, IIGU Ser. Matematika, 4:3 (2011), 171–172  mathnet

   2010
39. N. A. Sidorov, D. N. Sidorov, A. V. Krasnik, “On the solution of Volterra operator-integral equations in an irregular case by the method of successive approximations”, Differ. Uravn., 46:6 (2010), 874–882  crossref  mathscinet  zmath  isi (cited: 8)
40. N. A. Sidorov, D. N. Sidorov, “Solving the Hammerstein integral equation in the irregular case by successive approximations”, Siberian Math. J., 51:2 (2010), 325–329  mathnet  crossref  mathscinet  isi (cited: 8)  elib  elib  scopus (cited: 9)
41. N. A. Sidorov, A. V. Trufanov, “Nonlinear operator equations with functionaly modified argument”, IIGU Ser. Matematika, 3:4 (2010), 96–113  mathnet
42. N. A. Sidorov, D. N. Sidorov, “Branching solutions of nonlinear differential equations of $n$-th order”, IIGU Ser. Matematika, 3:1 (2010), 92–103  mathnet
43. N. A. Sidorov, R. Yu. Leont'ev, “On solutions with the maximal order of vanishing of nonlinear equations with a vector parameter in sectorial neighborhoods”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 226–237  mathnet  elib

   2009
44. N. A. Sidorov, A. V. Trufanov, “Nonlinear operator equations with functional perturbation of an argument of neutral type”, Differ. Uravn., 45:12 (2009), 1804–1808  crossref  mathscinet  zmath  isi (cited: 9)
45. N. A. Sidorov, D. N. Sidorov, “Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models”, Autom. Remote Control, 70:4 (2009), 598–604  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 2)

   2006
46. N. A. Sidorov, A. V. Trufanov, D. N. Sidorov, “Generalized solutions of nonlinear integral-functional equations”, Nelineĭn. Granichnye Zadachi, 16 (2006), 96–106  mathscinet  zmath
47. N. A. Sidorov, D. N. Sidorov, “Existence and construction of generalized solutions of nonlinear Volterra integral equations of the first kind”, Differ. Equ., 42:9 (2006), 1312–1316  mathnet  crossref  mathscinet  elib
48. Nikolai A. Sidorov, Michail V. Falaleev, Denis N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Bull. Malays. Math. Sci. Soc. (2), 29:2 (2006), 101–109  mathscinet  zmath

   2005
49. M. V. Falaleev, N. A. Sidorov, D. N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Lobachevskii J. Math., 20 (2005), 47–57  mathnet  mathscinet  zmath
50. M. V. Falaleev, N. A. Sidorov, “Continuous and generalized solutions of singular partial differential equations”, Lobachevskii J. Math., 20 (2005), 31–45  mathnet (cited: 1)  mathscinet  zmath  elib

   2003
51. N. A. Sidorov, A. V. Sinitsyn, “The stationary Vlasov-Maxwell system in bounded domains”, Nonlinear analysis and nonlinear differential equations (Russian), FizMatLit, Moscow, 2003, 50–88  mathscinet  zmath
52. N. A. Sidorov, V. A. Trenogin, “Bifurcation points of solutions of nonlinear equations”, Nonlinear analysis and nonlinear differential equations (Russian), FizMatLit, Moscow, 2003, 5–49  mathscinet  zmath
53. Michael V. Falaleev, Olga A. Romanova, Nicholas A. Sidorov, “Generalized Jordan sets in the theory of singular partial differential-operator equations”, Computational Science—{Iccs} 2003. Part II, Lecture Notes in Comput. Sci., 2658, Springer, Berlin, 2003, 523–532  crossref  mathscinet  zmath

   2002
54. N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov-Schmidt methods in nonlinear analysis and applications, Mathematics and its Applications, 550, Kluwer Academic Publishers, Dordrecht, 2002  crossref  mathscinet
55. N. A. Sidorov, V. R. Abdullin, “Intertwined branching equations in the theory of nonlinear equations”, Sobolev-type equations (Russian), Chelyab. Gos. Univ., Chelyabinsk, 2002, 83–115  mathscinet

   2001
56. N. A. Sidorov, “Parametrization of simple branching solutions of full rank and iterations in nonlinear analysis”, Russian Math. (Iz. VUZ), 45:9 (2001), 55–61  mathnet  mathscinet  zmath  elib
57. N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations in the theory of non-linear equations”, Sb. Math., 192:7 (2001), 1035–1052  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib  scopus (cited: 1)
58. V. R. Abdullin, N. A. Sidorov, “Interlaced equations in branching theory”, Dokl. Akad. Nauk, 377:3 (2001), 295–297  mathnet  mathscinet  zmath

   2000
59. B. V. Loginov, D. G. Rakhimov, N. A. Sidorov, “Development of M. K. Gavurin's pseudoperturbation method”, Operator theory and its applications (Winnipeg, MB, 1998), Fields Inst. Commun., 25, Amer. Math. Soc., Providence, RI, 2000, 367–381  mathscinet  zmath

   1999
60. N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations and invariance in the theory of nonlinear equations”, Symmetry and perturbation theory (Rome, 1998), World Sci. Publ., River Edge, NJ, 1999, 309–313  mathscinet  zmath
61. N. A. Sidorov, “The initial-value problem for differential equations with a Fredholm operator in the principal part”, Vestnik Chelyabinsk. Univ. Ser. 3 Mat. Mekh., 1999, no. 2(5), 103–112  mathscinet
62. N. A. Sidorov, A. V. Sinitsyn, “Index theory in the bifurcation problem of solutions of the Vlasov–Maxwell system”, Matem. Mod., 11:9 (1999), 83–100  mathnet  mathscinet  zmath
63. N. A. Sidorov, A. V. Sinitsyn, “On bifurcation points of the stationary Vlasov-Maxwell system with bifurcation direction”, Progress in Industrial Mathematics At {Ecmi} 98 (Gothenburg), European Consort. Math. Indust., Teubner, Stuttgart, 1999, 295–302  mathscinet
64. N. A. Sidorov, Vestnik Chelyabinsk. Gos. Univ., 1999, no. 5, 103–112  mathnet

   1997
65. N. A. Sidorov, “Implicit parametrization of solutions of the bifurcation equation”, Boundary value problems (Russian), Irkutsk. Gos. Univ., Irkutsk, 1997, 176–186, 207  mathscinet
66. N. A. Sidorov, A. V. Sinitsyn, “Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov–Maxwell system”, Math. Notes, 62:2 (1997), 223–243  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib
67. N. A. Sidorov, “An $N$-step iterative method in the theory of the branching of solutions of nonlinear equations”, Siberian Math. J., 38:2 (1997), 330–341  mathnet  crossref  mathscinet  zmath  isi (cited: 1)
68. B. V. Loginov, N. A. Sidorov, Yu. B. Rusak, Matem. Mod., 9:10 (1997), 30–31  mathnet  zmath

   1996
69. N. A. Sidorov, A. V. Sinitsyn, “Nontrivial solutions and bifurcation points of the Vlasov-Maxwell system”, Dokl. Akad. Nauk, 349:1 (1996), 26–28  mathnet (cited: 2)  mathscinet  zmath
70. N. A. Sidorov, A. V. Sinitsyn, “On the branching of solutions of the Vlasov–Maxwell system”, Siberian Math. J., 37:6 (1996), 1199–1211  mathnet  crossref  mathscinet  zmath  isi (cited: 2)

   1995
71. N. A. Sidorov, “Explicit and implicit parametrizations in the construction of branching solutions by iterative methods”, Sb. Math., 186:2 (1995), 297–310  mathnet  crossref  mathscinet  zmath  isi (cited: 10)

   1994
72. N. A. Sidorov, “Explicit parametrization of the solutions of nonlinear equations in a neighborhood of a branching point”, Dokl. Math., 49:3 (1994), 568–571  mathnet  mathscinet  zmath
73. N. A. Sidorov, O. A. Romanova, E. B. Blagodatskaya, “Partial differential equations with an operator of finite index at the principal part”, Differ. Equ., 30:4 (1994), 676–678  mathnet  zmath

   1992
74. N. A. Sidorov, O. A. Romanova, E. B. Blagodatskaya, “Differential equations with an operator of finite index in the main part”, Approximate methods for solving operator equations (Russian), Irkutsk. Gos. Ped. Inst., Irkutsk, 1992, 75–79  mathscinet
75. N. A. Sidorov, D. A. Tolstonogov, “Asymptotics and iterations in a neighborhood of the branching points of the solution of nonlinear equations”, Numerical methods in optimization and analysis (Russian) (Irkutsk, 1989), “Nauka” Sibirsk. Otdel., Novosibirsk, 1992, 162–171  mathscinet  zmath
76. V. A. Trenogin, N. A. Sidorov, “Potentiality conditions for a branching equation and bifurcation points of nonlinear operators”, Uzbek. Mat. Zh., 1992, no. 2, 40–49  mathscinet
77. Y. Markov, G. Rudykh, N. Sidorov, A. Sinitsyn, D. Tolstonogov, “Steady-state solutions of the Vlasov-Maxwell system and their stability”, Acta Appl. Math., 28:3 (1992), 253–293  crossref  mathscinet  zmath  isi (cited: 13)
78. N. A. Sidorov, E. B. Blagodatskaya, “Differential equations with a Fredholm operator in the main differential expression”, Dokl. Math., 44:1 (1992), 302–305  mathnet  mathscinet  zmath  isi
79. B. V. Loginov, N. A. Sidorov, “Group symmetry of the Lyapunov–Schmidt branching equation and iterative methods in the problem of a bifurcation point”, Math. USSR-Sb., 73:1 (1992), 67–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 5)

   1990
80. Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitzin, “Some families of solutions of the Vlasov-Maxwell system and their stability”, The Lyapunov functions method and applications, Imacs Ann. Comput. Appl. Math., 8, Baltzer, Basel, 1990, 197–203  mathscinet
81. Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Some families of solutions of the Vlasov–Maxwell system and their stability”, Matem. Mod., 2:12 (1990), 88–101  mathnet  mathscinet  zmath
82. V. A. Trenogin, N. A. Sidorov, B. V. Loginov, “Potentiality, group symmetry and bifurcation in the theory of branching equation”, Differential Integral Equations, 3:1 (1990), 145–154  mathscinet  zmath
83. V. A. Trenogin, N. A. Sidorov, B. V. Loginov, “The bifurcation equation: potentiality, bifurcation, symmetry”, Dokl. Math., 40:3 (1990), 517–520  mathnet  mathscinet  zmath  isi

   1989
84. Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Existence of stationary solutions of Vlasov–Maxwell equations and some of their exact solutions”, Matem. Mod., 1:6 (1989), 95–107  mathnet  mathscinet  zmath
85. G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Nonstationary solutions of the two-particle Vlasov–Maxwell system”, Dokl. Math., 34:8 (1989), 700–701  mathnet  mathscinet  isi
86. G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Bifurcating stationary solutions of a two-particle Vlasov-Maxwell system”, Dokl. Math., 34:2 (1989), 122–123  mathnet  mathscinet  isi

   1988
87. G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Some exact solutions of a stationary system of Vlasov-Maxwell equations”, Problems in the qualitative theory of differential equations (Russian) (Irkutsk, 1986), “Nauka” Sibirsk. Otdel., Novosibirsk, 1988, 118–128, 283  mathscinet
88. G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Stationary solutions of a system of Vlasov–Maxwell equations”, Dokl. Math., 33:9 (1988), 673–674  mathnet  mathscinet  isi

   1987
89. N. A. Sidorov, M. V. Falaleev, “Generalized solutions of degenerate differential and integral equations in Banach spaces”, The method of Lyapunov functions in the analysis of the dynamics of systems (Irkutsk, 1985) (Russian), “Nauka” Sibirsk. Otdel., Novosibirsk, 1987, 308–318, 328  mathscinet
90. V. A. Trenogin, B. V. Doginov, N. A. Sidorov, Proceedings of the Eleventh International Conference on Nonlinear Oscillations (Budapest, 1987), János Bolyai Math. Soc., Budapest, 1987, 502–505  mathscinet
91. N. A. Sidorov, M. V. Falaleev, “Generalized solution of differential equations with a Fredholm operator at the derivative”, Differ. Uravn., 23:4 (1987), 726–728  mathnet  zmath

   1985
92. B. V. Loginov, N. A. Sidorov, “A general method for the construction of the Lyapunov-Schmidt bifurcation equation, and some methods for its investigation”, Nonclassical problems of mathematical physics (Russian), “Fan”, Tashkent, 1985, 113–145, 232  mathscinet

   1984
93. N. A. Sidorov, “Lyapunov's methods in the theory of differential equations with a Volterra operator multiplying the derivative”, The method of Lyapunov functions and its applications, “Nauka” Sibirsk. Otdel., Novosibirsk, 1984, 241–251  mathscinet
94. N. A. Sidorov, “A class of degenerate differential equations with convergence”, Math. Notes, 35:4 (1984), 300–305  mathnet  crossref  mathscinet  zmath  isi (cited: 9)
95. N. A. Sidorov, “Differential equations with a Volterra operator multiplying the derivative”, Soviet Math. (Iz. VUZ), 28:1 (1984), 95–104  mathnet  mathscinet  zmath

   1983
96. B. V. Loginov, N. A. Sidorov, “Methods for the construction and use of the Lyapunov-Schmidt branching equation in the non-Fredholm case”, Theory and methods for solving ill-posed problems and their applications (Samarkand, 1983), Novosibirsk. Gos. Univ., Novosibirsk, 1983, 256–259  mathscinet
97. N. A. Sidorov, O. A. Romanova, “Application of certain results of branching theory in the solution of degenerate differential equations”, Differ. Uravn., 19:9 (1983), 1516–1526  mathnet  mathscinet

   1982
98. N. A. Sidorov, Obshchie voprosy regulyarizatsii v zadachakh teorii vetvleniya, Irkutsk. Gos. Univ., Irkutsk, 1982  mathscinet  zmath
99. N. A. Sidorov, “Solution of integro-differential equations with noninvertible operator multiplying the derivative”, Approximate methods for solving operator equations and their applications, Akad. Nauk Sssr Sibirsk. Otdel., Ènerget. Inst., Irkutsk, 1982, 121–130  mathscinet
100. O. A. Romanova, N. A. Sidorov, “The role of Schmidt's lemma and pseudoinverse operators in the theory of differential equations with degeneration”, Analytic methods in the theory of elliptic equations, “Nauka” Sibirsk. Otdel., Novosibirsk, 1982, 82–88  mathscinet

   1981
101. N. A. Sidorov, O. A. Romanova, “Theorems on the existence of solutions for differential equations with degeneration and discontinuous right-hand side”, Discrete and distributed systems, Irkutsk. Gos. Univ., Irkutsk, 1981, 78–89, 223  mathscinet  zmath
102. N. A. Sidorov, “Branching of solutions of nonlinear equations with a potential branching equation”, Dokl. Akad. Nauk Sssr, 256:6 (1981), 1322–1326  mathnet  mathscinet  mathscinet  zmath  isi

   1980
103. N. A. Sidorov, V. A. Trenogin, “Regularization of linear controls on the basis of perturbation theory”, Differ. Uravn., 16:11 (1980), 2039–2049  mathnet  mathscinet  zmath

   1979
104. N. A. Sidorov, “Regularization of an inverse boundary value problem”, Application of the methods of functional analysis to problems of mathematical physics and numerical analysis (Russian), Akad. Nauk Sssr Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1979, 123–128  mathscinet

   1978
105. N. A. Sidorov, “The calculation of eigenvalues and -vectors of linear operators on the basis of the theory of perturbations”, Differ. Uravn., 14:8 (1978), 1522–1525  mathnet  mathscinet  zmath
106. V. A. Trenogin, N. A. Sidorov, “Regularization of simple solutions of nonlinear equations in the neighborhood of a bifurcation point”, Siberian Math. J., 19:1 (1978), 128–132  mathnet  crossref  mathscinet  zmath  isi
107. N. A. Sidorov, “Regularization of linear differential equations with constant operators in the degenerate case”, Differ. Uravn., 14:3 (1978), 556–560  mathnet  mathscinet  zmath

   1977
108. N. A. Sidorov, “Integral systems of branching of degenerate differential equations”, Questions in applied mathematics (Russian), Sibirsk. Ènerget. Inst., Akad. Nauk Sssr Sibirsk. Otdel., Irkutsk, 1977, 177–179  mathscinet
109. N. A. Sidorov, “The method of continuation with respect to the parameter in the neighborhood of a branch point”, Questions in applied mathematics (Russian), Sibirsk. Ènerget. Inst., Akad. Nauk Sssr Sibirsk. Otdel., Irkutsk, 1977, 109–113  mathscinet
110. N. A. Sidorov, “Two-step regularization of the computation of the solutions of nonlinear equations in the neighborhood of a bifurcation point”, Partial differential equations and their applications (Russian), Izdat. “Fan” Uzbek. SSR, Tashkent, 1977, 120–129, 183  mathscinet
111. B. V. Loginov, N. A. Sidorov, “Calculation of the eigenvalues and eigenelements of linear operators by the method of false perturbations”, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 1977, no. 5, 26–29, 102  mathscinet  zmath
112. V. A. Trenogin, N. A. Sidorov, “Regularisation of computation of branching solutions of nonlinear equations”, Singular perturbations and boundary layer theory (Proc. Conf., École Centrale, Lyon, 1976), Springer, Berlin, 1977, 491–505. Lecture Notes in Math., Vol. 594  crossref  mathscinet

   1976
113. N. A. Sidorov, “A study of the continuous solutions of the Cauchy problem in the neighborhood of a branch point”, Soviet Math. (Iz. VUZ), 20:9 (1976), 77–87  mathnet  mathscinet  zmath
114. B. V. Loginov, N. A. Sidorov, “Calculation of eigenvalues and eigenvectors of bounded operators by the false-perturbation method”, Math. Notes, 19:1 (1976), 62–64  mathnet  crossref  mathscinet  zmath
115. N. A. Sidorov, V. A. Trenogin, “A certain approach to the problem of regularization on the basis of the perturbation of linear operators”, Math. Notes, 20:5 (1976), 976–979  mathnet  crossref  mathscinet  zmath
116. N. A. Sidorov, “The optimal choice of initial approximations to solutions of regularized equations in the theory of branching”, Math. Notes, 20:2 (1976), 710–713  mathnet  crossref  mathscinet  zmath
117. V. A. Trenogin, N. A. Sidorov, “Tihonov regularization of the problem of bifurcation points of nonlinear operators”, Siberian Math. J., 17:2 (1976), 314–323  mathnet  crossref  mathscinet  zmath  isi
118. N. A. Sidorov, V. A. Trenogin, “Regularization of the computation of the real solutions of nonlinear equations in the neighborhood of a branch point”, Dokl. Akad. Nauk Sssr, 228:5 (1976), 1049–1052  mathnet  mathscinet  zmath  isi (cited: 3)

   1975
119. N. A. Sidorov, V. A. Trenogin, “Regularization in the sense of A. N. Tihonov of some problems in bifurcation theory”, Differential and integral equations, No. 3 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1975, 183–193, 302  mathscinet
120. N. A. Sidorov, “Investigation of linear differential equations with constant operators in the degenerate case”, Differential and integral equations, No. 3 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1975, 178–182, 302  mathscinet

   1973
121. N. A. Sidorov, “Variational methods in the theory of the bifurcation points of nonlinear operators”, Differential and integral equations, No. 2 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1973, 255–270, 315–316  mathscinet
122. N. A. Sidorov, “The branching of the solutions of differential equations with a degeneracy”, Differ. Uravn., 9:8 (1973), 1464–1481  mathnet  mathscinet  zmath

   1972
123. V. A. Trenogin, N. A. Sidorov, “An investigation of the bifurcation points and nontrivial branches of the solutions of nonlinear equations”, Differential and integral equations, No. 1 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1972, 216–247  mathscinet
124. N. A. Sidorov, “The Cauchy problem for a certain class of differential equations”, Differ. Uravn., 8:8 (1972), 1521–1524  mathnet  mathscinet  zmath

   1969
125. N. A. Sidorov, L. V. Zorik, “The investigation of a certain integral equation with deviating argument”, Trudy Irkutsk. Gos. Univ., 64 (1969), 36–41  mathscinet

   1968
126. N. A. Sidorov, “The singular solutions of a certain class of integro-partial differential equations”, Trudy Irkutsk. Gos. Univ., 26 (1968), 36–45  mathscinet
127. N. A. Sidorov, “The branch points and singular solutions of certain classes of integral and integro-differential equations with two parameters”, Trudy Irkutsk. Gos. Univ., 26 (1968), 66–73  mathscinet
128. N. A. Sidorov, “Solution of the Cauchy problem for a certain class of integro-differential equations with analytic nonlinearities”, Differ. Uravn., 4:7 (1968), 1309–1316  mathnet  mathscinet  zmath

   1967
129. N. A. Sidorov, “A solution of a certain class of nonlinear integro-partial differential equations”, Proc. Sixth Interuniv. Sci. Conf. of the Far East on Physics and Mathematics, Vol. 3: Differential and Integral Equations (Russian), Habarovsk. Gos. Ped. Inst., Khabarovsk, 1967, 174–179  mathscinet
130. N. A. Sidorov, “The branching of the solutions of certain classes of integro-differential equations”, Proc. Sixth Interuniv. Sci. Conf. of the Far East on Physics and Mathematics, Vol. 3: Differential and Integral Equations (Russian), Habarovsk. Gos. Ped. Inst., Khabarovsk, 1967, 167–173  mathscinet
131. N. A. Sidorov, “Branching of solutions of the Cauchy problem for a class of nonlinear integro-differential equations”, Differ. Uravn., 3:9 (1967), 1592–1601  mathnet  mathscinet  zmath

   1966
132. N. A. Sidorov, “Application of a Newton diagram to the determination of singular solutions of integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 276–277  mathscinet
133. N. A. Sidorov, “The singular solutions of certain classes of integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 72–77  mathscinet
134. N. A. Sidorov, “The branching of the solutions of the Cauchy problem for a certain class of nonlinear integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 27–46  mathscinet

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