Stability analysis for first-order nonlinear differential equations with three-point boundary conditions
In the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the b...
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| Language: | English |
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EJAAM
2020-06-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2020/10.2478-ejaam-2020-0004.pdf |
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| author | Kamala E. Ismayilova |
| author_facet | Kamala E. Ismayilova |
| author_sort | Kamala E. Ismayilova |
| collection | DOAJ |
| description | In the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. The uniqueness theorem is proved by Banach fixed point principle, and the existence theorem is based on Schafer’s theorem. Then, we describe different types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability. We discuss the stability results providing suitable example. |
| format | Article |
| id | doaj-art-b4eb3013f3ee4935ae38a488ca377f36 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2020-06-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-b4eb3013f3ee4935ae38a488ca377f362025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902020-06-01202010.2478/ejaam-2020-0004Stability analysis for first-order nonlinear differential equations with three-point boundary conditionsKamala E. Ismayilova0Baku Engineering University, Khirdalan city, 120, AZ0102, Absheron, Baku, AzerbaijanIn the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. The uniqueness theorem is proved by Banach fixed point principle, and the existence theorem is based on Schafer’s theorem. Then, we describe different types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability. We discuss the stability results providing suitable example.https://ejaam.org/articles/2020/10.2478-ejaam-2020-0004.pdfthree-point boundary conditionsulam-hyers stabilityexistence and uniquenessfixed point theorems |
| spellingShingle | Kamala E. Ismayilova Stability analysis for first-order nonlinear differential equations with three-point boundary conditions E-Journal of Analysis and Applied Mathematics three-point boundary conditions ulam-hyers stability existence and uniqueness fixed point theorems |
| title | Stability analysis for first-order nonlinear differential equations with three-point boundary conditions |
| title_full | Stability analysis for first-order nonlinear differential equations with three-point boundary conditions |
| title_fullStr | Stability analysis for first-order nonlinear differential equations with three-point boundary conditions |
| title_full_unstemmed | Stability analysis for first-order nonlinear differential equations with three-point boundary conditions |
| title_short | Stability analysis for first-order nonlinear differential equations with three-point boundary conditions |
| title_sort | stability analysis for first order nonlinear differential equations with three point boundary conditions |
| topic | three-point boundary conditions ulam-hyers stability existence and uniqueness fixed point theorems |
| url | https://ejaam.org/articles/2020/10.2478-ejaam-2020-0004.pdf |
| work_keys_str_mv | AT kamalaeismayilova stabilityanalysisforfirstordernonlineardifferentialequationswiththreepointboundaryconditions |