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Existence of semi linear impulsive neutral evolution inclusions with infinite delay in Fréchet spaces. (English) Zbl 1349.34253

Summary: In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Fréchet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We study a new phase space for impulsive system with infinite delay.

MSC:

34K09 Functional-differential inclusions
34K45 Functional-differential equations with impulses
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