Existence and compactness of solution of semilinear integro-differential equations with finite delay

F. Sahraoui; А.  Ouahab

doi:10.37863/umzh.v74i9.7106

F. Sahraoui Laboratory Math., Sidi-Bel-Abbe`s Univ., Algeria
А. Ouahab Laboratory Math., Sidi-Bel-Abbe`s Univ., Algeria

DOI: https://doi.org/10.37863/umzh.v74i9.7106

Keywords: Mild solutions, resolvent operator, Banach fixed point, measure of non-compactness, attractivity.

Abstract

UDC 517.9

We present some existence and uniqueness results for a class of functional integro-differential evolution equations generated by the resolvent operator for which the semigroup is not necessarily compact. It is proved that the set of solutions is compact. Our approach is based on fixed point theory. Finally, some examples are given to illustrate the results.

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