Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions
The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the bounda...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2020-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/378 |
| _version_ | 1827395652727865344 |
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| author | M.J. Mardanov Y.A. Sharifov K.E. Ismayilova |
| author_facet | M.J. Mardanov Y.A. Sharifov K.E. Ismayilova |
| author_sort | M.J. Mardanov |
| collection | DOAJ |
| description |
The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem.
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| first_indexed | 2024-03-08T18:38:49Z |
| format | Article |
| id | doaj.art-3c67d7afcd3c44af924df86b9e3e2ffe |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:49Z |
| publishDate | 2020-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-3c67d7afcd3c44af924df86b9e3e2ffe2023-12-29T10:20:17ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112020-09-0199310.31489/2020m3/26-37Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditionsM.J. MardanovY.A. SharifovK.E. Ismayilova The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/378three-point boundary conditionsnonlinear integral boundary value problemsexistence and uniqueness of solutionsfixed point theorems |
| spellingShingle | M.J. Mardanov Y.A. Sharifov K.E. Ismayilova Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions Қарағанды университетінің хабаршысы. Математика сериясы three-point boundary conditions nonlinear integral boundary value problems existence and uniqueness of solutions fixed point theorems |
| title | Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions |
| title_full | Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions |
| title_fullStr | Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions |
| title_full_unstemmed | Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions |
| title_short | Existence and uniqueness of solutions for the system of integro-differential equations with three-point and nonlinear integral boundary conditions |
| title_sort | existence and uniqueness of solutions for the system of integro differential equations with three point and nonlinear integral boundary conditions |
| topic | three-point boundary conditions nonlinear integral boundary value problems existence and uniqueness of solutions fixed point theorems |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/378 |
| work_keys_str_mv | AT mjmardanov existenceanduniquenessofsolutionsforthesystemofintegrodifferentialequationswiththreepointandnonlinearintegralboundaryconditions AT yasharifov existenceanduniquenessofsolutionsforthesystemofintegrodifferentialequationswiththreepointandnonlinearintegralboundaryconditions AT keismayilova existenceanduniquenessofsolutionsforthesystemofintegrodifferentialequationswiththreepointandnonlinearintegralboundaryconditions |