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- W3173487684 abstract "Given a linear closed but not necessarily densely defined operator $A$ on a Banach space $E$ with nonempty resolvent set and a multivalued map $Fcolon Itimes Emap E$ with weakly sequentially closed graph, we consider the integro-differential inclusion begin{center} $dot{u}in Au+F(t,int u);;text{on }I,;;u(0)=x_0.$ end{center} We focus on the case when $A$ generates an integrated semigroup and obtain existence of integrated solutions in the sense of cite[Def.6.4.]{thieme} if $E$ is weakly compactly generated and $F$ satisfies [beta(F(t,Omega))<eta(t)beta(Omega);;text{for all bounded }Omegasubset E,] where $etain L^1(I)$ and $beta$ denotes the De Blasi measure of noncompactness. When $E$ is separable, we are able to show that the set of all integrated solutions is a compact $R_delta$-subset of the space $C(I,E)$ endowed with the weak topology. We use this result to investigate a nonlocal Cauchy problem described by means of a nonconvex-valued boundary condition operator. Some applications to partial differential equations with multivalued terms are also included." @default.
- W3173487684 created "2021-07-05" @default.
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- W3173487684 date "2021-01-01" @default.
- W3173487684 modified "2023-09-25" @default.
- W3173487684 title "Интегрированные решения неплотно определенных полулинейных интегро-дифференциальных включений: существование, топология и приложения" @default.
- W3173487684 doi "https://doi.org/10.4213/sm9331" @default.
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