Maksimov, Vladimir Petrovich

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Total publications: 38
Scientific articles: 33
Presentations: 1

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Full texts:1977
Doctor of physico-mathematical sciences (1985)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 16.05.1947
Keywords: functional differential equations, boundary value problems, control problems, constructive methods, reliable computing, mathematical modelling, mathematical economics.
UDC: 517.67, 517.91, 517.929, 517.927, 519.62
MSC: 34K05, 34K06, 34K10, 34K30, 34K35, 49K15, 49K25, 65L10, 65L80


An axiomatic description of the Cauchy matrix (kernel of the integral representations of solutions) is given, the adjoint boundary value problem to the general linear boundary value problem is constructed, a method of the study of nonlinear boundary value problems for the solvability with the use of a priori inequality is developed. Jointly with N. V. Azbelev and L. F. Rakhmatullina, the basics of the general theory of functional differential equations are worked out. In colloboration with A. N. Rumyantsev, the constructive methods for the study of boundary value problems, including impulsive ones, are developed with the use of reliable computations; the theory and the imlementation of the reliable computing experiment are worked out, which are aimed to the study of wide classes of problems including some problems in economic dynamics.


Graduated from the Izhevsk Mechanical Institute in 1970 (department of computer science). Ph.D. thesis was defended in 1974. D.Sci. thesis was defended in 1985. A list of my works contains more than 90 titles including 4 books (with coauthors). Since 1985 I, N. V. Azbelev, and L. F. Rakhmatullina have led the research seminar at the Perm State Technical University on functional differential equations.

In 1994 I was selected by the G. Soros International Scientific Fund as a George Soros professor. Since 1996 I am a member of the Academy of Nonlinear Sciences.

Main publications:
  • Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F. Introduction to the theory of linear functional differential equations. Atlanta: World Federation Publ., 1995.
  • Maksimov V. P., Rumyantsev A. N. The study of the solvability of boundary value problems for functional differential equations // Boundary Value Problems for Functional Differential Equations / ed. by J. Henderson. Singapore: World Scientific, 1995, 227–237.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. P. Maksimov, “To estimating linear functionals values over solutions of systems with aftereffect”, Russian Universities Reports. Mathematics, 25:131 (2020),  274–283  mathnet
2. V. P. Maksimov, “On a class of linear continuous-discrete systems with discrete memory”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:3 (2020),  385–395  mathnet  isi
3. V. P. Maksimov, “On the construction and estimates of the Cauchy matrix for systems with aftereffect”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019),  153–162  mathnet  elib
4. V. P. Maksimov, “The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:1 (2019),  40–51  mathnet  isi  elib
5. V. P. Maksimov, “On a class of optimal control problems for functional differential systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:1 (2018),  131–142  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S114–S124  isi  scopus
6. V. P. Maksimov, “Attainable values of on-target functionals for a functional differential system with impulses”, Tambov University Reports. Series: Natural and Technical Sciences, 23:123 (2018),  441–447  mathnet  elib
7. V. P. Maksimov, “Reliable computing experiment in the study of functional-differential equations: theory and applications”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  64–67  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 230:5 (2018), 712–716  scopus
8. V. P. Maksimov, “Some questions of the control theory for functional differential systems”, Izv. IMI UdGU, 2015, 2(46),  112–119  mathnet  elib
9. V. P. Maksimov, “On guaranteed estimate of reconstruction error of parameters of linear difference system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, 10,  72–76  mathnet; Russian Math. (Iz. VUZ), 59:10 (2015), 61–64  scopus
10. V. P. Maksimov, “Control of functional differential system in conditions of impulse disturbances”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, 9,  70–74  mathnet; Russian Math. (Iz. VUZ), 57:9 (2013), 58–61  scopus
11. V. P. Maksimov, “Functional differential continuous-discrete systems”, Izv. IMI UdGU, 2012, 1(39),  88–89  mathnet
12. V. P. Maksimov, A. L. Chadov, “A class of controls for a functional-differential continuous-discrete system”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, 9,  72–76  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:9 (2012), 62–65  scopus
13. V. P. Maksimov, A. L. Chadov, “The constructive investigation of boundary-value problems with approximate satisfaction of boundary conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, 10,  82–86  mathnet  mathscinet; Russian Math. (Iz. VUZ), 54:10 (2010), 71–74  scopus
14. N. V. Azbelev, V. P. Maksimov, P. M. Simonov, “Functional differential equations and their applications”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, 1,  3–23  mathnet  elib
15. A. D. Andrianov, V. P. Maksimov, P. M. Simonov, “Краевые задачи для разностных моделей”, Matem. Mod. Kraev. Zadachi, 3 (2008),  20–23  mathnet
16. V. P. Maksimov, P. M. Simonov, “Functional differential equations and their applications”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 2,  87–90  mathnet
17. V. P. Maksimov, “Problems of impulsive and mixed control for linear functional differential systems”, Izv. IMI UdGU, 2006, 3(37),  87–88  mathnet
18. V. P. Maksimov, “Control problems for linear functional differential systems. Constructive approach, computer-assisted study, applications”, Izv. IMI UdGU, 2006, 2(36),  73–78  mathnet
19. V. P. Maksimov, A. N. Rumyantsev, “Convincing computational experiment in the study of functional differential systems”, Izv. IMI UdGU, 2002, 2(25),  61–64  mathnet
20. V. P. Maksimov, “Some problems of a regularization for overdetermined boundary value problems of economics dynamics”, Matem. Mod., 9:2 (1997),  57–65  mathnet  mathscinet  zmath
21. V. P. Maksimov, A. N. Rumyantsev, “Boundary value problems and problems of impulse control in economic dynamics. Constructive investigation”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, 5,  56–71  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:5 (1993), 48–62
22. S. A. Gusarenko, E. S. Zhukovskiy, V. P. Maksimov, “On the theory of functional-differential equations with locally Volterra operators”, Dokl. Akad. Nauk SSSR, 287:2 (1986),  268–272  mathnet  mathscinet  zmath
23. V. P. Maksimov, “Some nonlinear boundary value problems”, Differ. Uravn., 19:3 (1983),  396–414  mathnet  mathscinet
24. N. V. Azbelev, V. P. Maksimov, “Equations with retarded argument”, Differ. Uravn., 18:12 (1982),  2027–2050  mathnet  mathscinet
25. V. P. Maksimov, “On passage to the limit in boundary value problems for functional-differential equations”, Differ. Uravn., 17:11 (1981),  1984–1994  mathnet  mathscinet
26. A. I. Bulgakova, V. P. Maksimov, “Functional and functional-differential inclusions with Volterra operators”, Differ. Uravn., 17:8 (1981),  1362–1374  mathnet  mathscinet
27. N. V. Azbelev, V. P. Maksimov, “A priori estimates of the solutions of the Cauchy problem and the solvability of boundary value problems for equations with retarded argument”, Differ. Uravn., 15:10 (1979),  1731–1747  mathnet  mathscinet  zmath
28. V. P. Maksimov, “The connectedness of a set of solutions of a functional-differential equation”, Differ. Uravn., 14:7 (1978),  1179–1185  mathnet  mathscinet  zmath
29. V. P. Maksimov, L. F. Rakhmatullina, “A conjugate equation for a general linear boundary value problem”, Differ. Uravn., 13:11 (1977),  1966–1973  mathnet  mathscinet  zmath
30. V. P. Maksimov, “The Cauchy formula for a functional-differential equation”, Differ. Uravn., 13:4 (1977),  601–606  mathnet  mathscinet  zmath
31. V. P. Maksimov, “The property of being Noetherian of the general boundary value problem for a linear functional differential equation”, Differ. Uravn., 10:12 (1974),  2288–2291  mathnet  mathscinet  zmath
32. V. P. Maksimov, L. F. Rakhmatullina, “A linear functional-differential equation that is solved with respect to the derivative”, Differ. Uravn., 9:12 (1973),  2231–2240  mathnet  mathscinet  zmath
33. V. P. Maksimov, L. F. Rakhmatullina, “The representation of the solutions of a linear functional-differential equation”, Differ. Uravn., 9:6 (1973),  1026–1036  mathnet  mathscinet  zmath

34. A. V. Arutyunov, M. V. Borzova, E. O. Burlakov, A. A. Grigorenko, E. S. Zhukovskiy, S. E. Zhukovskiy, V. P. Maksimov, E. A. Panasenko, E. A. Pluzhnikova, A. V. Ponosov, V. M. Tikhomirov, O. V. Filippova, I. A. Finogenko, Yu. G. Fomicheva, A. G. Chentsov, A. I. Shindyapin, “In memory of professor Alexander Ivanovich Bulgakov”, Russian Universities Reports. Mathematics, 25:129 (2020),  100–102  mathnet
35. A. A. Gryzlov, V. A. Zaitsev, D. M. Kinzebulatov, N. V. Latypova, V. P. Maksimov, N. N. Petrov, S. N. Popova, V. I. Rodionov, L. I. Rodina, Yu. M. Smetanin, D. L. Fedorov, “Vasilii Yakovlevich Derr. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019),  612–617  mathnet
36. I. V. Gaishun, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, N. Kh. Rozov, T. K. Shemjakina, “N. V. Azbelev (A tribute on the occasion of his 80th birthday)”, Differ. Uravn., 38:7 (2002),  867–869  mathnet  mathscinet; Differ. Equ., 38:7 (2002), 917–919
37. N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, T. K. Shemjakina, “Nikolaǐ Viktorovich Azbelev (on the occasion of his seventy-fifth birthday)”, Differ. Uravn., 33:4 (1997),  435–439  mathnet  mathscinet; Differ. Equ., 33:4 (1997), 433–438
38. N. P. Erugin, N. A. Izobov, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, “Nikolaǐ Viktorovich Azbelev (on the occasion of his sixtieth birthday)”, Differ. Uravn., 18:4 (1982),  725–730  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. К оценке значений линейных функционалов на решениях систем с последействием
В. П. Максимов
International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information Technologies of Derzhavin Tambov State University
October 13, 2020 11:00   

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