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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2016-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/241/abstr.html |
| _version_ | 1811345053740695552 |
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| author | Pengyu Chen Xuping Zhang Yongxiang Li |
| author_facet | Pengyu Chen Xuping Zhang Yongxiang Li |
| author_sort | Pengyu Chen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T19:58:22Z |
| format | Article |
| id | doaj.art-6a7b313b212640ff923ae635298d0742 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T19:58:22Z |
| publishDate | 2016-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-6a7b313b212640ff923ae635298d07422022-12-22T02:32:17ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-09-012016241,111Existence of mild solutions to partial differential equations with non-instantaneous impulsesPengyu Chen0Xuping Zhang1Yongxiang Li2 Northwest Normal Univ., Lanzhou, China Northwest Normal Univ., Lanzhou, China Northwest Normal Univ., Lanzhou, China 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.http://ejde.math.txstate.edu/Volumes/2016/241/abstr.htmlEvolution equationinitial value problemnon-instantaneous impulsemild solutionequicontinuous semigroupexistence of solutions |
| spellingShingle | Pengyu Chen Xuping Zhang Yongxiang Li Existence of mild solutions to partial differential equations with non-instantaneous impulses Electronic Journal of Differential Equations Evolution equation initial value problem non-instantaneous impulse mild solution equicontinuous semigroup existence of solutions |
| title | Existence of mild solutions to partial differential equations with non-instantaneous impulses |
| title_full | Existence of mild solutions to partial differential equations with non-instantaneous impulses |
| title_fullStr | Existence of mild solutions to partial differential equations with non-instantaneous impulses |
| title_full_unstemmed | Existence of mild solutions to partial differential equations with non-instantaneous impulses |
| title_short | Existence of mild solutions to partial differential equations with non-instantaneous impulses |
| title_sort | existence of mild solutions to partial differential equations with non instantaneous impulses |
| topic | Evolution equation initial value problem non-instantaneous impulse mild solution equicontinuous semigroup existence of solutions |
| url | http://ejde.math.txstate.edu/Volumes/2016/241/abstr.html |
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