Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

Abstract

In this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

Keywords

• integro-differential equations
• finite delay
• mild solution
• state-dependent delay
• semigroup theory
• resolvent operator
• kuratowski measure of noncompactness
• state-dependent delay
• nonlocal initial conditions