Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses
In this paper, we consider a non-instantaneous impulsive system represented by second order nonlinear differential equation with deviated argument in a Banach space X. We used the strongly continuous cosine family of linear operators and Banach fixed point method to study the existence and uniquenes...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018-04-01
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| Series: | Journal of King Saud University: Science |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364716305511 |
| _version_ | 1828810230501212160 |
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| author | Malik Muslim Avadhesh Kumar Michal Fečkan |
| author_facet | Malik Muslim Avadhesh Kumar Michal Fečkan |
| author_sort | Malik Muslim |
| collection | DOAJ |
| description | In this paper, we consider a non-instantaneous impulsive system represented by second order nonlinear differential equation with deviated argument in a Banach space X. We used the strongly continuous cosine family of linear operators and Banach fixed point method to study the existence and uniqueness of the solution of the non-instantaneous impulsive system. Also, we study the existence and uniqueness of the solution of the nonlocal problem and stability of the non-instantaneous impulsive system. Finally, we give examples to illustrate the application of these abstract results. Keywords: Non-instantaneous impulses, Deviated argument, Banach fixed point theorem |
| first_indexed | 2024-12-12T09:08:45Z |
| format | Article |
| id | doaj.art-fffd3ff1e22a4d78860557b89ae6878c |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-12-12T09:08:45Z |
| publishDate | 2018-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-fffd3ff1e22a4d78860557b89ae6878c2022-12-22T00:29:35ZengElsevierJournal of King Saud University: Science1018-36472018-04-01302204213Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulsesMalik Muslim0Avadhesh Kumar1Michal Fečkan2School of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175 005, IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175 005, IndiaDepartment of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia; Corresponding author.In this paper, we consider a non-instantaneous impulsive system represented by second order nonlinear differential equation with deviated argument in a Banach space X. We used the strongly continuous cosine family of linear operators and Banach fixed point method to study the existence and uniqueness of the solution of the non-instantaneous impulsive system. Also, we study the existence and uniqueness of the solution of the nonlocal problem and stability of the non-instantaneous impulsive system. Finally, we give examples to illustrate the application of these abstract results. Keywords: Non-instantaneous impulses, Deviated argument, Banach fixed point theoremhttp://www.sciencedirect.com/science/article/pii/S1018364716305511 |
| spellingShingle | Malik Muslim Avadhesh Kumar Michal Fečkan Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses Journal of King Saud University: Science |
| title | Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses |
| title_full | Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses |
| title_fullStr | Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses |
| title_full_unstemmed | Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses |
| title_short | Existence, uniqueness and stability of solutions to second order nonlinear differential equations with non-instantaneous impulses |
| title_sort | existence uniqueness and stability of solutions to second order nonlinear differential equations with non instantaneous impulses |
| url | http://www.sciencedirect.com/science/article/pii/S1018364716305511 |
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