Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators

摘要

This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed-point theorem for condensing maps combined with theories of analytic resolvent operators, we prove some existence theorems. As an application of these main theorems, some practical consequences are derived. Keywords Impulsive differential equations - Neutral integro-differential equations - State-dependent delays - Analytic resolvents Communicated by F. Zirilli.