Existence solutions for nondensely integrodifferential equations with state-dependent delay

Abstract

In this work, we study the existence of mild solutions for some nondensely partial functional integro-differential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely defined and generates an integrated resolvant operators. The nonlinear part satisfies Carathéodory’s conditions. Our approach is based on the generalized Darbo Fixed Point Theorem on Banach spaces and the integrated resolvent operators theory. For illustration, we propose a reaction–diffusion equation with state-dependent delay. The results obtained in this paper are a generalization of some existing results in this area.