Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulsions: Existence and Qualitative Results

Abstract

This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral and state-dependent delay problems. Our criteria were obtained by applying a Darbo’s fixed-point theorem combined with measures of noncompactness. The obtained result is illustrated by an example at the end.

Keywords

• attractivity
• controllability
• fixed point
• infinite delay
• integrodifferential equation
• measures of noncompactness