Semilinear Integro-differential Evolution Equations with Delay via Densifiability Techniques

Abstract

In this study, we investigate the existence of solutions for a specific type of semilinear integro-differential evolution equations occurring in Banach spaces, incorporating both finite and state-dependent delays. Our approach introduces a novel fixed-point theorem centered on the notion of the degree of nondensifiability. To illustrate our findings, we present an illustrative example that demonstrates the key outcomes of our analysis.