New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

Abstract

This paper investigates a functional integral differential equation with state-dependent delay in Banach spaces. This equation's linear part depends on time and generates a linear evolution system. Using the resolvent operator and fixed-point methods theory, we formulate a new set of sufficient conditions for mild solutions of functional integral-differential equations with state-dependent delays. The next part of this study examines the attractiveness of mild solutions for the system under consideration. Finally, we give an example to illustrate the theoretical results.