Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions
This paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uni...
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| Language: | English |
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EJAAM
2019-07-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2018/10.2478-ejaam-2018-0003.pdf |
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| author | Mısır J. Mardanov, Yagub A. Sharifov Kamala E. Ismayilova |
| author_facet | Mısır J. Mardanov, Yagub A. Sharifov Kamala E. Ismayilova |
| author_sort | Mısır J. Mardanov, |
| collection | DOAJ |
| description | This paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples. |
| format | Article |
| id | doaj-art-ef122314f0094aeda8b1f9b940c9e46d |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2019-07-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-ef122314f0094aeda8b1f9b940c9e46d2025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902019-07-01201810.2478/ejaam-2018-0003Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditionsMısır J. Mardanov,0Yagub A. Sharifov1Kamala E. Ismayilova2Institute of Mathematics and Mechanics of NAS of Azerbaijan, AzerbaijanInstitute of Mathematics and Mechanics of NAS of Azerbaijan, Baku State University, AzerbaijanBaku Engineering University, Khirdalan city, 120 AZ0102, Absheron, Baku, AzerbaijanThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.https://ejaam.org/articles/2018/10.2478-ejaam-2018-0003.pdfthree-point boundary conditionsexistenceuniquenessfixed pointimpulsive differential equations |
| spellingShingle | Mısır J. Mardanov, Yagub A. Sharifov Kamala E. Ismayilova Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions E-Journal of Analysis and Applied Mathematics three-point boundary conditions existence uniqueness fixed point impulsive differential equations |
| title | Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions |
| title_full | Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions |
| title_fullStr | Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions |
| title_full_unstemmed | Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions |
| title_short | Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions |
| title_sort | existence and uniqueness of solutions for nonlinear impulsive differential equations with three point boundary conditions |
| topic | three-point boundary conditions existence uniqueness fixed point impulsive differential equations |
| url | https://ejaam.org/articles/2018/10.2478-ejaam-2018-0003.pdf |
| work_keys_str_mv | AT mısırjmardanov existenceanduniquenessofsolutionsfornonlinearimpulsivedifferentialequationswiththreepointboundaryconditions AT yagubasharifov existenceanduniquenessofsolutionsfornonlinearimpulsivedifferentialequationswiththreepointboundaryconditions AT kamalaeismayilova existenceanduniquenessofsolutionsfornonlinearimpulsivedifferentialequationswiththreepointboundaryconditions |