Existence and Uniqueness of $\varrho$-Mild Solutions for Integrodifferential Equations with State-Dependent Nonlocal Conditions

Abstract

In this paper, we present some results related to the existence and uniqueness of mild solutions for a class of integrodifferential equations with state-dependent nonlocal conditions using analytic resolvent operators. We assume that the resolvent operator is not compact. Our results were derived through the application of the $\varrho$-norm, measures of noncompactness, and fixed-point theory. Additionally, we demonstrate the compactness of the set of solutions. In the final section, we illustrate our obtained results with an example to demonstrate their applicability.