Main scientific interests lay in the sphere of contemporary multivalued analysis and its applications. The problems of construction of the topological coincidence degree theory for various classes of multivalued maps. The applications of topological methods in the theory of differential inclusions were studied. In particular, the method of guiding functions and its modifications to periodic problem of differential and functional differential inclusions were aplied.
Main publications:
Obukhovskii V., Zecca P., Loi N.V. and Kornev S., Method of Guiding Functions in Problems of Nonlinear Analysis, Lecture Notes in Math., 2076, Springer, 2013
V. G. Zvyagin, S. V. Kornev, “Method of guiding functions for existence problems for periodic solutions of differential equations”, Journal of Mathematical Sciences, 233:4 (2018), 578–601
3.
S. V. Kornev, “On the Method of Multivalent Guiding Functions for Periodic Solutions of Differential Inclusions”, Autom. Remote Control, 64:3 (2003), 409–419
4.
S. V. Kornev, V. V. Obukhovskii, “Localization of the method of guiding functions in the problem about periodic solutions of differential inclusions”, Russian Math. (Iz. VUZ), 53:5 (2009), 19–27
5.
S. V. Kornev, “Multivalent guiding function in a problem on existence of periodic solutions of some classes of differential inclusions”, Russian Math. (Iz. VUZ), 60:11 (2016), 11–21
6.
S. V. Kornev, “Nonsmooth integral directing functions in the problems of forced oscillations”, Autom. Remote Control, 76:9 (2015), 1541–1550
7.
S. V. Kornev, V. V. Obukhovskii, “Non-smooth guiding potentials in problems on forced oscillations”, Autom. Remote Control, 68:1 (2007), 1–8
8.
S. V. Kornev, V. V. Obukhovskii, “On Nonsmooth Multivalent Guiding Functions”, Differential Equations, 39:11 (2003), 1578–1584
9.
S. Kornev , V. Obukhovskii, J. C. Yao, “On asymptotics of solutions for a class of functional differential inclusions”, Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 34:2 (2014), 219–227
N. V. Loi, V. Obukhovskii, S. Kornev, “Existence and Global Bifurcation of solutions for a Class of Operator-Differential Inclusions”, Differential Equations and Dynamical Systems, 20:3 (2012), 285–300
S. V. Kornev, V. V. Obukhovskii, “Asymptotic behavior of solutions of differential inclusions and the method of guiding functions”, Differential Equations, 51:6 (2015), 700-705 (to appear)
12.
S. Kornev, V. Obukhovskii, P. Zecca, “On multivalent guiding functions method in the periodic problem for random differential equations”, Journal of Dynamics and Differential Equations, 31:2 (2019), 1017–1028
S. Kornev, V. Obukhovskii, P. Zecca, “Guiding functions and periodic solutions for inclusions with causal multioperators”, Applicable Analysis, 96:3 (2017), 418–428
S. Kornev, Y.-C. Liou, “Method of multivalent guiding functions in the bifurcation problem of differential inclusions”, The Journal of Nonlinear Science and Applications, 9:8 (2016), 5259–5270
V. G. Zvyagin, S. V. Kornev, “Existence of an attractor for three-dimensional model of the Bingham fluid motion”, Russian Math. (Iz. VUZ), 60:1 (2016), 64–67
16.
V. V. Obukhovskii, S. V. Kornev, E. N. Getmanova, “O topologicheskikh kharakteristikakh dlya nekotorykh klassov mnogoznachnykh otobrazhenii”, Chebyshevskii sbornik, 21:2 (2020), 291–309
S. Kornev, V. Obukhovskii, J. C. Yao, “Random integral guiding functions in the periodic problem for random differential inclusions with causal multioperators”, Journal of Differential Equations, 268:10 (2020), 5792–5810
S. V. Kornev, “Method of nonsmooth integral guiding functions in periodic solutions problem for inclusions with causal multioperators”, Bulletin of the South Ural State University, Series «Mathematical Modelling, Programming & Computer Software», 9:2 (2016), 46–59
19.
V. Obukhovskii, S. Kornev, P. Korneva, “Method of guiding functions and Birkhoff-Kellogg-Rothe and Kakutani fixed point theorems”, Communications in Optimization Theory, 8 (2024), 1-7
20.
S. V. Kornev, P. S. Korneva, N. E. Iakusheva, “On approach to the study of the periodic problem for random differential equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 5, 82–88
21.
E. N. Getmanova , P. S. Korneva , S. V. Kornev, “Periodicheskie resheniya sluchainykh funktsionalno-differentsialnykh vklyuchenii s normalnoi pravoi chastyu”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2023, no. 1, 69-84
22.
E. N. Getmanova , P. S. Korneva , S. V. Kornev, “Periodicheskie resheniya sluchainykh funktsionalno-differentsialnykh vklyuchenii s normalnoi pravoi chastyu”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2023, no. 1, 69-84
23.
V. Obukhovskii , S. Kornev , Ek. Getmanova, “On a random topological characteristic for inclusions with nonlinear Fredholm operators: applications to some classes of feedback control systems”, Advances in Systems Science and Applications, 23:3 (2023), 48-65
24.
S. V. Kornev, M. M. Kulmanakova, E. L. Ulyanova, “Negladkie sluchainye integralnye potentsialy v zadache ob asimptoticheskom povedenii reshenii sluchainykh funktsionalno-differentsialnykh vklyuchenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2022, 1, 35–46
25.
Y. E. Gliklikh, S. V. Kornev, V. V. Obukhovskii, “Integral operators, guiding potentials and periodic solutions of differential inclusions on non-compact Lie groups”, Journal of Mathematical Sciences, 266 (2022), 667–674
26.
V. V. Obukhovskii, S. V. Kornev, E. N. Getmanova, “On the relative fixed point index for a class of noncompact multivalued maps”, Russian Math. (Iz. VUZ), 65:5 (2021), 48–59
27.
Yu. E. Bezmelnitsyna, S. V. Kornev, V. V. Obukhovskii, “Method of stochastic multivalent guiding functions in a periodic problem for stochastic differential inclusions”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 194, VINITI, Moscow, 2021, 38–45
28.
S. Kornev, V. Obukhovskii, Yu. Bezmelnitsyna, J.-C. Yao, “On asymptotics of solutions for inclusions with random causal multioperators”, Journal of Nonlinear and Convex Analysis, 22:1 (2021), 173-184
29.
S. Kornev, V. Obukhovskii, Ek. Getmanova, N.-Ch. Wong, “On periodic solutions for a class of random differential inclusions”, Journal of Nonlinear and Convex Analysis, 22:8 (2021), 1615-1626
30.
M. Kamenskii, S. Kornev, V. Obukhovskii, N.-Ch. Wong, “On bounded solutions of semilinear fractional order differential inclusions in Hilbert spaces”, Journal of Nonlinear and Variational Analysis, 5:2 (2021), 251-265
31.
V. V. Obukhovskii, S. V. Kornev, E. N. Getmanova, “Ob operatore sdviga po traektoriyam reshenii sluchainykh differentsialnykh vklyuchenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2021, no. 4, 81-89
32.
Yu. E. Bezmelnitsyna, V. V. Obukhovskii, S. V. Kornev, “Metod sluchainykh mnogolistnykh napravlyayuschikh funktsii v periodicheskoi zadache dlya sluchainykh differentsialnykh vklyuchenii”, Itogi nauki i tekhniki. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory, 194 (2021), 38–45
33.
S. Kornev, V. Obukhovskii, J. C. Yao, “Nonsmooth integral guiding potentials and asymptotic behavior of solutions for inclusions with causal multioperators”, Optimization, 69:2 (2020), 345–355
34.
E. N. Getmanova, S. V. Kornev, “Some applications of the theory of random degree of coincidence in periodic problems for functional differential inclusions”, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 186, VINITI, Moscow, 2020, 21–31
35.
Yu. E. Bezmelnitsyna, S. V. Kornev, V. V. Obukhovskii, “Nonsmooth integral direction potentials in the problem of the asymptotic behavior of trajectories of some classes of functional differential inclusions”, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 186, VINITI, Moscow, 2020, 13–20
36.
Yu. E. Bezmelnitsyna, S. V. Kornev, V. V. Obukhovskii, “Negladkie integralnye napravlyayuschie potentsialy i asimptoticheskoe povedenie traektorii funktsionalno-differentsialnykh vklyuchenii s normalnymi pravymi chastyami”, Vestnik RAEN, 19:2 (2019), 34-35
37.
E. N. Getmanova, S. V. Kornev, V. V. Obukhovskii, “O nekotorykh primeneniyakh teorii sluchainoi stepeni sovpadeniya v zadache o suschestvovanii periodicheskikh reshenii differentsialnykh vklyuchenii”, Vestnik RAEN, 19:2 (2019), 53-55
38.
Yu. Gliklikh, S. Kornev, V. Obukhovskii, “Guiding potentials and periodic solutions of differential equations on manifolds”, Global and Stochastic Analysis, 6:1 (2019), 1-7
39.
S. V. Kornev, N. V. Loi, V. V. Obukhovskii, C.-F. Wen, “Random nonsmooth integral guiding functions and asymptotic behavior of trajectories for random differential inclusions”, Journal of Nonlinear and Convex Analysis, 19:3 (2018), 493–500
40.
V. G. Zvyagin, S. V. Kornev, Metod napravlyayuschikh funktsii i ego modifikatsii, URSS, Moskva, 2018 , 168 pp.
41.
S. V. Kornev, V. V. Obukhovskii, “Integralnye napravlyayuschie potentsialy v zadache ob asimptoticheskom povedenii reshenii funktsionalno-differentsialnykh vklyuchenii”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 23:121 (2018), 31–43
42.
S. V. Kornev, V. V. Obukhovskii, “Asymptotic behavior of solutions for inclusions with causal multioperators and the method of integral guiding potentials”, Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki, 23:122 (2018), 136–144
43.
S. Kornev , V. Obukhovskii, P. Zecca, “Generalized integral guiding functions and periodic solutions for inclusions with causal multioperators”, Stochastic Modeling and Applications, 22:2 (2018), 73-84
44.
V. Obukhovskii, M. Kamenskii, S. Kornev, Y.-C. Liou, “On asymptotics of solutions for a class of differential inclusions with a regular right-hand part”, Journal of Nonlinear and Convex Analysis, 18:5 (2017), 967–975
45.
S. V. Kornev, Y.-C. Liou, N. V. Loi, V. V. Obukhovskii, “On periodic solutions of random differential inclusions”, Applied Analysis and Optimization, 1:2 (2017), 245–258
46.
S. V. Kornev, V. V. Obukhovskii, “Integralnye napravlyayuschie funktsii i periodicheskie resheniya vklyuchenii s kauzalnymi operatorami”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 9:1 (2016), 55–65
47.
S. V. Kornev, “Asimptoticheskoe povedenie reshenii differentsialnykh vklyuchenii s nevypukloi pravoi chastyu”, Vestnik Voronezhskogo gos. un-ta. Ser. Fizika, matematika, 2016, no. 1, 96–104
48.
S. V. Kornev, “Napravlyayuschie funktsii na zadannom mnozhestve v zadache o suschestvovanii periodicheskikh reshenii differentsialnykh vklyuchenii s nevypukloi pravoi chastyu”, Vestnik Voronezhskogo gos. un-ta. Ser. Fizika, matematika, 2016, no. 2, 107–122
49.
S. V. Kornev, N. V. Loi, “Metod mnogolistnykh napravlyayuschikh funktsii v zadache o bifurkatsii reshenii differentsialnykh uravnenii”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 21:2 (2016), 390–401
50.
S. V. Kornev, “The method of generalized integral guiding function in the periodic problem of differential inclusions”, IIGU Ser. Matematika, 13 (2015), 16–31
51.
S. V. Kornev, “Nabor mnogolistnykh napravlyayuschikh funktsii v zadache o periodicheskikh resheniyakh nekotorykh klassov differentsialnykh vklyuchenii”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 20:4 (2015), 835–842
52.
S. V. Kornev, “O nekotorykh obobscheniyakh metoda mnogolistnoi napravlyayuschei funktsii v zadache o suschestvovanii periodicheskikh reshenii nekotorykh klassov differentsialnykh vklyuchenii”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 20 (2015), 1214–1216
53.
S. V. Kornev, “O negladkikh integralnykh napravlyayuschikh funktsiyakh v issledovanii asimptoticheskogo povedeniya reshenii funktsionalno-differentsialnykh uravnenii”, Izvestiya VGPU, 268:3 (2015), 182–184
54.
S. Kornev, V. Obukhovskii, “On some developments of the method of integral guiding functions”, Functional Differential Equations, 12:3-4 (2005), 303–310
55.
S. V. Kornev, V. V. Obukhovskii, “O nekotorykh variantakh teorii topologicheskoi stepeni dlya nevypukloznachnykh multiotobrazhenii”, Trudy matematicheskogo fakulteta, Voronezhskii gosuniversitet, 2004, 56–74
56.
S. V. Kornev , V. V. Obukhovskii, “O nekotorykh obobscheniyakh metoda napravlyayuschei funktsii v zadache o periodicheskikh resheniyakh differentsialnykh vklyuchenii”, Vestnik Tambovskogo gos. un-ta. Ser. Estestvennye i tekhnicheskie nauki, 8:3 (2003), 399
57.
S. V. Kornev, V. V. Obukhovskii, “O nekotorykh razvitiyakh metoda negladkikh mnogolistnykh napravlyayuschikh funktsii”, Matematicheskie modeli i operatornye uravneniya, 2, Voronezhskii gosuniversitet, Voronezh, 2003, 75–90
58.
S. V. Kornev, V. V. Obukhovskii, “Ob integralnykh napravlyayuschikh funktsiyakh dlya funktsionalno-differentsialnykh vklyuchenii”, Topologicheskie metody nelineinogo analiza, Voronezhskii gosuniversitet, Voronezh, 2000, 87–107
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