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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 309–327 (Mi izv1242)

On the problem of periodic solutions of operator differential inclusions

V. S. Klimov

Abstract: Geometric methods of studying the problem of periodic solutions of differential inclusions are developed, and the notion of rotation of the vector field generated by a multivalued operator of parabolic type is introduced. Properties of the rotation are established, and applications to existence theorems for periodic solutions are given. Variants of the relationship principle are proved, as well as Bogolyubov's second theorem for operator differential inclusions. Possible applications are connected with the mechanics of viscoplastic media, extremal problems, and the theory of differential equations with deviating argument.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 317–335

Bibliographic databases:

UDC: 517.911
MSC: Primary 34A60, 34C25, 34G20; Secondary 54C60, 35K99

Citation: V. S. Klimov, “On the problem of periodic solutions of operator differential inclusions”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 309–327; Math. USSR-Izv., 34:2 (1990), 317–335

Citation in format AMSBIB
\Bibitem{Kli89} \by V.~S.~Klimov \paper On the problem of periodic solutions of operator differential inclusions \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 2 \pages 309--327 \mathnet{http://mi.mathnet.ru/izv1242} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=998298} \zmath{https://zbmath.org/?q=an:0697.47055} \transl \jour Math. USSR-Izv. \yr 1990 \vol 34 \issue 2 \pages 317--335 \crossref{https://doi.org/10.1070/IM1990v034n02ABEH000648} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. S. Klimov, “Evolution parabolic inequalities with multivalued operators”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 365–380
2. M. Yu. Kokurin, “Asymptotic behavior of periodic solutions of parabolic equations with weakly nonlinear perturbation”, Math. Notes, 57:3 (1995), 261–265
3. V. S. Klimov, “Evolution problems in the mechanics of visco-plastic media”, Izv. Math., 59:1 (1995), 141–157
4. V. S. Klimov, “A regularization method for evolutionary problems in mechanics of visco-plastic media”, Math. Notes, 62:4 (1997), 405–413
5. V. S. Klimov, “Bounded solutions of differential inclusions with homogeneous principal parts”, Izv. Math., 64:4 (2000), 755–776
6. V. S. Klimov, “The averaging method in the problem of periodic solutions of quasilinear parabolic equations”, Russian Math. (Iz. VUZ), 45:10 (2001), 36–43
7. Klimov V.S., “On differential inclusions with homogeneous principal part”, Differential Equations, 38:10 (2002), 1472–1480
8. V. S. Klimov, “Averaging of parabolic inclusions”, Sb. Math., 195:1 (2004), 19–34
9. V. S. Klimov, “Monotone mappings and flows of viscous media”, Siberian Math. J., 45:6 (2004), 1063–1074
10. V. S. Klimov, “Stability Theorems in the First-Order Approximation for Differential Inclusions”, Math. Notes, 76:4 (2004), 478–489
11. Klimov, VS, “Periodic Solutions of Evolution Equations with Homogeneous Principal Part”, Differential Equations, 44:8 (2008), 1101
12. N. A. Demyankov, V. S. Klimov, “Ob odnom klasse operatornykh vklyuchenii”, Model. i analiz inform. sistem, 19:3 (2012), 63–72
13. Ricardo Gama, Georgi Smirnov, “Stability and Optimality of Solutions to Differential Inclusions via Averaging Method”, Set-Valued Var. Anal, 2013
14. V. S. Klimov, “Operator Inclusions and Quasi-Variational Inequalities”, Math. Notes, 101:5 (2017), 863–877
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