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Nondensely defined evolution impulsive differential inclusions with nonlocal conditions. (English) Zbl 1039.34056
The authors study a problem for evolution impulsive differential inclusions with nonlocal conditions of the form $y'(t) \in Ay(t) + F(t,y(t))$, $t \in J=[0,b]$, $t \neq t_k$, $k=1,\dots,m$, $y(t_k^+)-y(t_k^-)= I_k(y(t_k^-))$, $k=1,\dots,m$, $y(0)+g(y)=y_0$, where $A:D(A)\subset E \to E$ is a nondensely defined closed linear operator, $F:J \times E \to P(E)$ is a multivalued map with nonempty values, $g:C(J',E) \to E$ ($J'=J-\{t_1,\dots,t_m\}$), $I_k:E \to \overline{D(A)} $ are functions, $y_0 \in E$ and $E$ is a separable Banach space. The authors establish sufficient conditions for the existence of integral solutions for the convex and for the nonconvex case by using fixed-point theorems and a selection theorem.

MSC:
34G25Evolution inclusions
34A37Differential equations with impulses
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