Existence of mild solutions to partial differential equations with non-instantaneous impulses

Abstract

In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth condition and a noncompactness measure condition. Also we assume the non-instantaneous impulsive functions satisfy some Lipschitz conditions. An example is given to illustrate our results.

Keywords

• Evolution equation
• initial value problem
• non-instantaneous impulse
• mild solution
• equicontinuous semigroup
• existence of solutions