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

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

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 t...

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Bibliographic Details
Main Authors: Pengyu Chen, Xuping Zhang, Yongxiang Li
Format: Article
Language:English
Published: Texas State University 2016-09-01
Series:Electronic Journal of Differential Equations
Subjects:
Evolution equation
initial value problem
non-instantaneous impulse
mild solution
equicontinuous semigroup
existence of solutions
Online Access:http://ejde.math.txstate.edu/Volumes/2016/241/abstr.html
Description
Summary: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.
ISSN:1072-6691

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