On the stability of first order impulsive evolution equations
In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presente...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2014-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol34/3/art/opuscula_math_3439.pdf |
| _version_ | 1819054226410569728 |
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| author | JinRong Wang Michal Fečkan Yong Zhou |
| author_facet | JinRong Wang Michal Fečkan Yong Zhou |
| author_sort | JinRong Wang |
| collection | DOAJ |
| description | In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presented by using an impulsive integral inequality of the Gronwall type. Two examples are also provided to illustrate our results. Finally, some extensions of the Ulam-Hyers-Rassias stability for the case with infinite impulses are given. |
| first_indexed | 2024-12-21T12:48:15Z |
| format | Article |
| id | doaj.art-fc413b50a8bc49ec8407b4ef07176a77 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-21T12:48:15Z |
| publishDate | 2014-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-fc413b50a8bc49ec8407b4ef07176a772022-12-21T19:03:34ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742014-01-01343639657http://dx.doi.org/10.7494/OpMath.2014.34.3.6393439On the stability of first order impulsive evolution equationsJinRong Wang0Michal Fečkan1Yong Zhou2Guizhou University, Department of Mathematics, Guiyang, Guizhou 550025, P.R. ChinaComenius University, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, SlovakiaXiangtan University, Department of Mathematics, Xiangtan, Hunan 411105, P.R. ChinaIn this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presented by using an impulsive integral inequality of the Gronwall type. Two examples are also provided to illustrate our results. Finally, some extensions of the Ulam-Hyers-Rassias stability for the case with infinite impulses are given.http://www.opuscula.agh.edu.pl/vol34/3/art/opuscula_math_3439.pdffirst orderimpulsive evolution equationsUlam-Hyers-Rassias stability |
| spellingShingle | JinRong Wang Michal Fečkan Yong Zhou On the stability of first order impulsive evolution equations Opuscula Mathematica first order impulsive evolution equations Ulam-Hyers-Rassias stability |
| title | On the stability of first order impulsive evolution equations |
| title_full | On the stability of first order impulsive evolution equations |
| title_fullStr | On the stability of first order impulsive evolution equations |
| title_full_unstemmed | On the stability of first order impulsive evolution equations |
| title_short | On the stability of first order impulsive evolution equations |
| title_sort | on the stability of first order impulsive evolution equations |
| topic | first order impulsive evolution equations Ulam-Hyers-Rassias stability |
| url | http://www.opuscula.agh.edu.pl/vol34/3/art/opuscula_math_3439.pdf |
| work_keys_str_mv | AT jinrongwang onthestabilityoffirstorderimpulsiveevolutionequations AT michalfeckan onthestabilityoffirstorderimpulsiveevolutionequations AT yongzhou onthestabilityoffirstorderimpulsiveevolutionequations |