We suggest new methods of solving the periodical problem for a non-linear object governed by a functional differential inclusion $x^\prime (t) \in F(t,x_t)$ under the assumption that the multimap $F$ has convex compact values and satisfies upper Carath\'eodory conditions as well as the case when it is non-convex-valued and is a normal multimap. The class of normal multimaps includes into itself, for example, bounded almost lower semicontinuous multimaps with compact values and multimaps satisfying Carath\'eodory conditions. In both cases, to study the problem under consideration, we apply the generalized integral guiding function
The method of a generalized integral guiding function in the problem of existence of periodic solutions to functional differential inclusions / Kornev, Andrey; Obukhovskii, Valeri; Zecca, Pietro. - In: DIFFERENCIALʹNYE URAVNENIÂ. - ISSN 0374-0641. - STAMPA. - 52:(2016), pp. 1335-1344. [10.1134/S0012266116100049]
The method of a generalized integral guiding function in the problem of existence of periodic solutions to functional differential inclusions
ZECCA, PIETRO
2016
Abstract
We suggest new methods of solving the periodical problem for a non-linear object governed by a functional differential inclusion $x^\prime (t) \in F(t,x_t)$ under the assumption that the multimap $F$ has convex compact values and satisfies upper Carath\'eodory conditions as well as the case when it is non-convex-valued and is a normal multimap. The class of normal multimaps includes into itself, for example, bounded almost lower semicontinuous multimaps with compact values and multimaps satisfying Carath\'eodory conditions. In both cases, to study the problem under consideration, we apply the generalized integral guiding functionFile | Dimensione | Formato | |
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