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Zbl 1039.34056
Benchohra, M.; Gatsori, E. P.; Henderson, J.; Ntouyas, S. K.
Nondensely defined evolution impulsive differential inclusions with nonlocal conditions.
(English)
[J] J. Math. Anal. Appl. 286, No. 1, 307-325 (2003). ISSN 0022-247X

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.
[Francesca Papalini (Ancona)]
MSC 2000:
*34G25 Evolution inclusions
34A37 Differential equations with impulses

Keywords: nondensely defined operator; impulsive semilinear differential equation; existence; fixed point; nonlocal condition

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