Nonlinear semilinear integro-differential evolution equations with impulsive effects

Abstract

In this paper, we investigate the existence of a piecewise asymptotically almost automorphic mild solution to some classes of integro-differential equations with impulsive effects in Banach space. The working tools are based on the Mönch’s fixed point theorem, the concept of measures of noncompactness theorem and resolvent operator. In order to illustrate our main results, we study the piecewise asymptotically almost automorphic solution of the impulsive differential equations.

Keywords

• Asymptotically almost automorphic
• integro-differential equations
• mild solution
• evolution system
• Kuratowski measures of noncompactness
• Mönch fixed point

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