<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System
In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻U...
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MDPI AG
2019-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/2/231 |
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doaj-b2be5c0ac66f47eb87d00235852595f12020-11-25T00:33:26ZengMDPI AGSymmetry2073-89942019-02-0111223110.3390/sym11020231sym11020231<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive SystemXiaoming Wang0Muhammad Arif1Akbar Zada2School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, ChinaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanIn this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Ulam stability, <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam stability and <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam⁻Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.https://www.mdpi.com/2073-8994/11/2/231semilinear nonautonomous systeminstantaneous impulsesmild solution<i>β</i>–Hyers–Ulam– Rassias stability |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiaoming Wang Muhammad Arif Akbar Zada |
| spellingShingle |
Xiaoming Wang Muhammad Arif Akbar Zada <i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System Symmetry semilinear nonautonomous system instantaneous impulses mild solution <i>β</i>–Hyers–Ulam– Rassias stability |
| author_facet |
Xiaoming Wang Muhammad Arif Akbar Zada |
| author_sort |
Xiaoming Wang |
| title |
<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System |
| title_short |
<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System |
| title_full |
<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System |
| title_fullStr |
<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System |
| title_full_unstemmed |
<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System |
| title_sort |
<i>β</i>–hyers–ulam–rassias stability of semilinear nonautonomous impulsive system |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2019-02-01 |
| description |
In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Ulam stability, <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam stability and <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam⁻Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result. |
| topic |
semilinear nonautonomous system instantaneous impulses mild solution <i>β</i>–Hyers–Ulam– Rassias stability |
| url |
https://www.mdpi.com/2073-8994/11/2/231 |
| work_keys_str_mv |
AT xiaomingwang ibihyersulamrassiasstabilityofsemilinearnonautonomousimpulsivesystem AT muhammadarif ibihyersulamrassiasstabilityofsemilinearnonautonomousimpulsivesystem AT akbarzada ibihyersulamrassiasstabilityofsemilinearnonautonomousimpulsivesystem |
| _version_ |
1725316933200379904 |