Pengyu Chen, Xuping Zhang, Yongxiang Li
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.
Submitted March 7, 2016. Published September 1, 2016.
Math Subject Classifications: 34K45, 47D06.
Key Words: Evolution equation; initial value problem; non-instantaneous impulse;
mild solution; equicontinuous semigroup; existence of solutions.
Show me the PDF file (236 KB), TEX file for this article.
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Pengyu Chen Department of Mathematics Northwest Normal University Lanzhou 730070, China email: chpengyu123@163.com, Phone: +86 0931 7971111 |
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Xuping Zhang Department of Mathematics Northwest Normal University Lanzhou 730070, China email: lanyu9986@126.com |
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Yongxiang Li Department of Mathematics Northwest Normal University Lanzhou 730070, China email: liyx@nwnu.edu.cn |
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