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



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.


Impulsive differential equations Neutral integro-differential equations State-dependent delays Analytic resolvents 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematics, Physics & Software EngineeringLanzhou Jiaotong UniversityLanzhouChina

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