Loginov, Boris Vladimirovich

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Total publications: 41
Scientific articles: 39
Presentations: 2

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Doctor of physico-mathematical sciences (1983)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Keywords: linear and nonlinear functional analysis; nonlinear equations; branching theory of solutions of nonlinear equations; stability; symmetry in nonlinear analysis; applications to mathematical physics and natural sciences.


In 1964–1969 — works on spectral theory of linear operators (perturbations of discrete spectrum, numerical range and spectrum, von Neumann spectral sets, generalizations of normal operators). From 1969 — works on branching theory of solutions of nonlinear equations, mainly under group symmetry conditions. They were proved theorems about symmetry of basic nonlinear equation inheritance by branching equations (BEq). On their base group analysis of differential equations methods were applied to construction of BEq general form on allowing by its group symmetry both in stationary and nonstationary branching. Role of generalized Jordan structure of the linearized operator-function of bifurcational parameter in branching theory, recently in application to the construction and investigation of resolving systems in branching theory problems, in particular to BEq in the root subspaces. Applications to mathematical physics: phase transitions in statistical crystal theory; capillary-gravity surface waves in fluid layers; von Karman plate in supersonic gas flow; pseudoperturbation methods in spectral theory.


  1. Graduated from Faculty of Mathematics and Mechanics of V. I. Lenin Tashkent State University (TashSU) in 1961 (chair of Mathematical Analysis);
  2. Ph.D. thesis was defended in 1965 (V. I. Romanovsky Mathematical Institute Acad. Sci. UzbekSSR);
  3. 1965–1966 — assistent of "Math. Analysis" Chair of Tashkent State University, UzbekSSR;
  4. 1966–1985 — senior sci. contributor of "Differential Equations" Dept.;
  5. 1985–1993 — Head of "Applied Mathematics" Dept. V. I. Romanovsky Mathematical Institute, Academy of Sciences of Uzbekistan;
  6. 1993 — by the present time Professor of "Higher Mathematics" Chair, Ulyanovsk state technical University. A list of my works contains more than 200 titles.

Member-correspondent "Natural Sci" (1995); academician of "Nonlinear Sciences", International Academy (1997); member of GAMM (Gesellschaft fur Angewandte Mathematik and Mechanik) (1996); American Mathematical Society (1997); Middle-Volga Math. Society (Mordova, Saransk, 1996); Reviewer of RZ Matematika, Moscow, Russia (from 1972), Mathematical Reviews (from 1972), Zentralblatt fur Mathematik (from 1975); order "Sign of Honour" N 457134 (1986); supervisor of 13 kandidate phys.-math. sci. (Ph.D.).

Main publications:
  • Loginov B. V. Determination of the bifurcation equation by its group symmetry — Andronov–Hopf bifurcation // Nonlinear Analysis, TMA, 28(1997), 12, 2033–2047.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. L. R. Kim-Tyan, B. V. Loginov, Yu. B. Rousak, “Normal forms of the degenerate autonomous differential equations with the maximal Jordan chain and simple applications”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:3 (2017),  5–15  mathnet  isi  elib
2. B. V. Loginov, Yu. B. Rousak, L. R. Kim-Tyan, “Differential equations with degenerate, depending on the unknown function operator at the derivative”, CMFD, 59 (2016),  119–147  mathnet
3. P. A. Shamanaev, B. V. Loginov, “The branching of periodic solutions of inhomogeneous linear differential equations with a the perturbation in the form of small linear term with delay”, Zhurnal SVMO, 18:3 (2016),  61–69  mathnet  elib
4. A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “The branching of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and the disturbance in the form of small linear term”, Zhurnal SVMO, 18:1 (2016),  45–53  mathnet  elib
5. B. V. Loginov, Yu. B. Rousak, L. R. Kim-Tyan, “Normal forms of the degenerate differential autonomous and non autonomous equations with the maximal Jordan chain of length two and three”, The Bulletin of Irkutsk State University. Series Mathematics, 12 (2015),  58–71  mathnet
6. T. E. Badokina, B. V. Loginov, “Models of multiparameter bifurcations in boundary value problems for ODEs of the fourth order on divergence of elongated plate in supersonic gas flow”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015),  24–35  mathnet  isi  elib
7. A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “Comments to the problem on branching of periodical solutions at Andronov-Hopf bifurcation in differential equations with degenerated operator before the derivative”, Zhurnal SVMO, 16:4 (2014),  33–40  mathnet
8. A. V. Gerasimov, B. V. Loginov, N. N. Yuldashev, “Eigenvalue problem for the Laplace operator in $s$-dimensional unit ball $\Omega\subset\R^{s+1}$ with displacements in derivatives II”, Zhurnal SVMO, 16:4 (2014),  7–22  mathnet
9. , B. V. Loginov, “Cayley-Hamilton theorem for two variants of matrix spectral problems on E.Shmidt and development of characteristic polynomial”, Zhurnal SVMO, 16:3 (2014),  7–20  mathnet
10. I. V. Konopleva, B. V. Loginov, “Group Symmetry for Dynamica Bifurcation Problems with Schmidt Spectrum in Linearization”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:4 (2014),  50–63  mathnet
11. A. V. Gerasimov, B. V. Loginov, N. N. Yuldashev, “Eigenvalue problem for the Laplace operator with displacement in derivatives”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, 3(114),  41–45  mathnet
12. B. V. Loginov, N. N. Yuldashev, A. V. Gerasimov, “The eigenvalue problem for the Laplace operator in $s$-dimensional unit ball $\Omega$ with displacement in derivatives”, Zhurnal SVMO, 15:4 (2013),  136–147  mathnet
13. A. A. kjashkin, B. V. Loginov, P. A. Shamanaev, “Comments to the problems of small perturbations of linear equations and linear term of the spectral characteristics of a Fredholm operator”, Zhurnal SVMO, 15:3 (2013),  100–107  mathnet
14. B. V. Loginov, Yu. B. Rusak, L. R. Kim-Tyan, “Degenerated differential equations with variable degeneration operator”, Zhurnal SVMO, 15:3 (2013),  8–20  mathnet
15. T. E. Badokina, B. V. Loginov, Yu. B. Rusak, “Construction of the asymptotics of solutions of nonlinear boundary value problems for fourth order differential equation with two bifurcation parameters”, The Bulletin of Irkutsk State University. Series Mathematics, 5:1 (2012),  2–12  mathnet
16. B. V. Loginov, I. V. Konopleva, L. V. Mironova, “Dynamic bifurcation problems with E.Schmidt spectrum in the linearization under group symmetry conditions”, Zhurnal SVMO, 14:1 (2012),  25–35  mathnet
17. B. V. Loginov, L. R. Kim-Tyan, “Group symmetry of potential type bifurcation equations in dynamic branching”, Tr. Inst. Mat., 20:2 (2012),  75–83  mathnet
18. V. A. Trenogin, B. V. Loginov, L. R. Kim-Tyan, “Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace”, Trudy Mat. Inst. Steklova, 278 (2012),  260–268  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 251–259  isi  elib  scopus
19. B. V. Loginov, I. V. Konopleva, Y. B. Rousak, “Implicit operator theorems under group symmetry conditions”, The Bulletin of Irkutsk State University. Series Mathematics, 4:1 (2011),  31–43  mathnet
20. B. V. Loginov, V. E. Pospeev, “Regularization of the problem about perturbations of linear equation by small linear terms.}”, Zhurnal SVMO, 13:3 (2011),  146–147  mathnet
21. B. V. Loginov, I. V. Konopleva, L. V. Mironova, “Stationary bifurcation problems with E. Schmidt spectrum in linearization under group symmetry conditions.”, Zhurnal SVMO, 13:3 (2011),  15–30  mathnet
22. V. A. Trenogin, B. V. Loginov, L. R. Kim-Tyan, “Solutions stability on linear approximation to Cauchy problem , branching equation in the root subspace, symmetry”, Zhurnal SVMO, 12:3 (2010),  8–17  mathnet
23. B. V. Loginov, O. V. Makeev, “Bifurcation theory methods in problem about crystallization of liquid phase state in statistical crystal theory”, Trudy SVMO, 11:2 (2009),  194–196  mathnet
24. B. V. Loginov, O. V. Makeeva, “Pseudoperturbation operator in generalized eigenvalue problem under group symmetry”, Trudy SVMO, 11:2 (2009),  43–48  mathnet
25. B. V. Loginov, O. V. Makeev, “Bifurcation theory methods in problem about crystallization of liquid phase state in statistical crystal theory”, Trudy SVMO, 11:1 (2009),  10–28  mathnet
26. B. V. Loginov, O. V. Makeeva, “On application of pseudoperturbation method to the solving of algebraic equations”, Trudy SVMO, 10:1 (2008),  315–320  mathnet
27. I. V. Konopleva, B. V. Loginov, O. V. Makeev, Yu. B. Rusak, “Symmetry of $SO(2)$ and $SH(2)$ in Poincaré-Andronov-Hopf bifurcation problems with potential branching equations”, Trudy SVMO, 10:1 (2008),  106–112  mathnet
28. B. V. Loginov, I. V. Konopleva, Yu. B. Rusak, “Symmetry and potentiality in a general problem in bifurcation theory”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, 4,  30–40  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 50:4 (2006), 28–38
29. B. V. Loginov, O. V. Makeev, “Solutions with subgroup symmetry for singular equations in bifurcation theory”, Lobachevskii J. Math., 20 (2005),  91–101  mathnet  mathscinet  zmath
30. B. Karasözen, I. V. Konopleva, B. V. Loginov, “Differential-algebraic equations in the theory of invariant manifolds for singular equations”, Lobachevskii J. Math., 20 (2005),  77–89  mathnet  mathscinet  zmath
31. B. Karasozen, B. V. Loginov, “Invariant Reduction of Partially Potential Branching Equations and Iterative Methods in the Problem on a Bifurcation Point with a Symmetry”, Differ. Uravn., 40:3 (2004),  380–388  mathnet  mathscinet; Differ. Equ., 40:3 (2004), 410–419
32. B. V. Loginov, “Bifurcation and symmetry in problems of capillary-gravity waves”, Sibirsk. Mat. Zh., 42:4 (2001),  868–887  mathnet  mathscinet  zmath; Siberian Math. J., 42:4 (2001), 731–747  isi
33. B. V. Loginov, V. A. Trenogin, “A problem with a free boundary for the Laplace equation, capillary-gravitational waves in space, bifurcation and symmetry”, Differ. Uravn., 34:8 (1998),  1100–1106  mathnet  mathscinet; Differ. Equ., 34:8 (1998), 1104–1110
34. B. V. Loginov, N. A. Sidorov, Yu. B. Rusak, “Теоремы существования бифуркации в присутствии одной обобщенной жордановой цепочки нечетной длины”, Matem. Mod., 9:10 (1997),  30–31  mathnet  zmath
35. P. A. Vel'misov, B. V. Loginov, “Group analysis in twopoint boundary value problems describing the rod bending”, Matem. Mod., 7:5 (1995),  37–38  mathnet  zmath
36. B. V. Loginov, “Group analysis in problems with symmetry violatation”, Matem. Mod., 7:5 (1995),  36  mathnet  zmath
37. B. V. Loginov, “On the determination of a bifurcation equation by its symmetry group”, Dokl. Akad. Nauk, 331:6 (1993),  677–680  mathnet  mathscinet  zmath; Dokl. Math., 48:1 (1994), 200–205
38. B. V. Loginov, L. R. Kim-Tyan, Yu. B. Rusak, “Modification of the Lyapunov–Schmidt method and the stability of solutions of differential equations with a degenerate operator of finite index multiplying the derivative”, Dokl. Akad. Nauk, 330:6 (1993),  687–690  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 599–603
39. B. V. Loginov, N. A. Sidorov, “Group symmetry of the Lyapunov–Schmidt branching equation and iterative methods in the problem of a bifurcation point”, Mat. Sb., 182:5 (1991),  681–691  mathnet  mathscinet  zmath; Math. USSR-Sb., 73:1 (1992), 67–77  isi
40. V. A. Trenogin, N. A. Sidorov, B. V. Loginov, “The bifurcation equation: potentiality, bifurcation, symmetry”, Dokl. Akad. Nauk SSSR, 309:2 (1989),  286–289  mathnet  mathscinet  zmath; Dokl. Math., 40:3 (1990), 517–520
41. A. O. Kuznetsov, B. V. Loginov, “Construction of the asymptotic behavior of small solutions of a problem of rolling waves”, Dokl. Akad. Nauk SSSR, 304:6 (1989),  1320–1323  mathnet  mathscinet  zmath; Dokl. Math., 34:2 (1989), 107–108
42. B. V. Loginov, A. M. Nagornyi, “On the spectrum of a Bitsadze–Samarskiǐ problem”, Differ. Uravn., 24:11 (1988),  2012–2016  mathnet  mathscinet  zmath
43. B. V. Loginov, L. R. Kim-Tyan, “On the stability of bifurcating solutions”, Differ. Uravn., 24:4 (1988),  695–698  mathnet  mathscinet  zmath
44. B. V. Loginov, “On the use of vector invariants for determining the general form of a bifurcation equation under group invariance conditions”, Dokl. Akad. Nauk SSSR, 259:5 (1981),  1045–1050  mathnet  mathscinet  zmath
45. B. V. Loginov, D. G. Rakhimov, “On the connection between the method of false perturbations, analytical perturbations, and differential equations with degeneration”, Differ. Uravn., 17:11 (1981),  2090–2093  mathnet  mathscinet  zmath
46. B. V. Loginov, “Construction of periodic solutions of the three-dimensional problem of waves above a level bottom”, Dokl. Akad. Nauk SSSR, 247:2 (1979),  324–328  mathnet  mathscinet  zmath
47. B. V. Loginov, “On invariant solutions in branching theory”, Dokl. Akad. Nauk SSSR, 246:5 (1979),  1048–1051  mathnet  mathscinet  zmath
48. B. V. Loginov, “Variational methods in bifurcation theory under conditions of group invariance”, Differ. Uravn., 15:9 (1979),  1710–1712  mathnet  mathscinet  zmath
49. B. V. Loginov, N. A. Sidorov, “Calculation of eigenvalues and eigenvectors of bounded operators by the false-perturbation method”, Mat. Zametki, 19:1 (1976),  105–108  mathnet  mathscinet  zmath; Math. Notes, 19:1 (1976), 62–64
50. B. V. Loginov, “The branching of the solutions of the Cauchy problem for linear differential equations”, Differ. Uravn., 11:9 (1975),  1709–1712  mathnet  mathscinet  zmath
51. B. V. Loginov, V. A. Trenogin, “The use of group invariance in branching theory”, Differ. Uravn., 11:8 (1975),  1518–1521  mathnet  mathscinet  zmath
52. B. V. Loginov, “Branching of the solutions of the equation $\Delta u+\lambda u=f(u)$ on the sphere”, Differ. Uravn., 8:10 (1972),  1816–1824  mathnet  mathscinet  zmath
53. V. A. Trenogin, B. V. Loginov, “On the application of continuous groups in the theory of branching”, Dokl. Akad. Nauk SSSR, 197:1 (1971),  36–39  mathnet  mathscinet  zmath
54. B. V. Loginov, V. A. Trenogin, “The use of group properties to determine milti-parameter families of solutions of nonlinear equations”, Mat. Sb. (N.S.), 85(127):3(7) (1971),  440–454  mathnet  mathscinet  zmath; Math. USSR-Sb., 14:3 (1971), 438–452

55. E. N. Artem'eva, I. V. Boykov, M. A. Borisov, D. I. Boyarkin, P. A. Vel'misov, V. K. Gorbunov, T. A. Gorshunova, V. Z. Grines, Yu. N. Deryugin, E. V. Desyaev, D. K. Egorova, R. V. Zhalnin, O. E. Kaledin, V. N. Krizsky, E. B. Kuznetsov, B. V. Loginov, T. Ph. Mamedova, S. I. Martynov, N. D. Morozkin, S. M. Muryumin, I. P. Nikitin, O. V. Pochinka, D. V. Pashutkin, A. Yu. Pavlov, E. E. Peskova, I. P. Ryazantseva, V. I. Safonkin, G. A. Smolkin, S. I. Spivak, L. A. Sukharev, A. O. Syromyasov, M. T. Terekhin, V. F. Tishkin, S. A. Firsova, E. A. Chernoivanova, I. I. Chuchaev, P. A. Shamanaev, O. S. Yazovtseva, Z. Ya. Yakupov, “On the 80th anniversary of professor E.V. Voskresensky's birthday”, Zhurnal SVMO, 19:4 (2017),  95–99  mathnet
56. B. V. Loginov, V. V. Pukhnachev, G. A. Sviridyuk, A. V. Keller, S. A. Zagrebina, O. A. Romanova, D. N. Sidorov, A. Dreglea, R. Yu. Leontiev, “Nikolay Aleksandrovich Sidorov (to the 75th Anniversary)”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015),  143–148  mathnet  elib

Presentations in Math-Net.Ru
1. Bifurcation theory methods in multiparametric aerohydroelasticity problems
T. E. Badokina, A. A. kjashkin, B. V. Loginov
International Conference on Mathematical Control Theory and Mechanics
July 4, 2015 17:20
2. Differential equations with degenerate linearly dependent on unknown operator at the derivative
B. V. Loginov, Yu. B. Rusak, L. R. Kim-Tyan
International Conference on Differential Equations and Dynamical Systems
July 4, 2014 18:30

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