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ON SOME DEVELOPMENTS OF THE METHOD OF MULTIVALENT GUIDING FUNCTIONS IN THE PERIODIC PROBLEM FOR SOME CLASSES OF DIFFERENTIAL INCLUSIONS

Annotation

We consider the periodic problem for a nonlinear system governed by a differential inclusion with nonconvex right-hand side. In this paper, the notion of a complete and sharp set of generalized multivalent guiding functions and regular multivalent guiding function are defined. Application of the topological degree theory and these methods allows to establish the solvability of the periodic problem.

Keywords

differential inclusion; multivalent guiding function; periodic solutions; topological degree

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UDC

517.911.5

Pages

1214-1216

References

1. Krasnosel'skiy M.A. Operator sdviga po traektoriyam differentsial'nykh uravneniy. M.: Nauka, 1966. 2. Rachinskiy D.I. Vynuzhdennye kolebaniya v sistemakh upravleniya v usloviyakh, blizkikh k rezonansu // AiT. 1995. № 11. S. 87-98. 3. Krasnoselskii A.M., Krasnoselskii M.A., Mawhin J., Pokrovskii A.V. Generalized guiding functions in a problem on high frequency forced oscillations // Nonlinear Anal. Theory, Methods Appl. 1994. V. 22. № 11. P. 1357-1371. 4. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskiy V.V. Vvedenie v teoriyu mnogoznachnykh otobrazheniy i differentsial'nykh vklyucheniy. M.: Librokom, 2011. 5. Gґorniewicz L. Topological Fixed Point Theory of Multivalued Mappings. Berlin: Springer, 2006.

Received

2015-05-13

Section of issue

Scientific articles

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