Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability
We consider the two-point boundary value problems for a nonlinear one-dimensional second-order differential equation with involution in the second derivative and in lower terms. The questions of existence and uniqueness of the classical solution of two-point boundary value problems are studied. The...
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| Format: | Article |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231340?viewType=HTML |
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| author | Abdissalam Sarsenbi Abdizhahan Sarsenbi |
| author_facet | Abdissalam Sarsenbi Abdizhahan Sarsenbi |
| author_sort | Abdissalam Sarsenbi |
| collection | DOAJ |
| description | We consider the two-point boundary value problems for a nonlinear one-dimensional second-order differential equation with involution in the second derivative and in lower terms. The questions of existence and uniqueness of the classical solution of two-point boundary value problems are studied. The definition of the Green's function is generalized for the case of boundary value problems for the second-order linear differential equation with involution, indicating the points of discontinuities and the magnitude of discontinuities of the first derivative. Uniform estimates for the Green's function of the linear part of boundary value problems are established. Using the contraction mapping principle and the Schauder fixed point theorem, theorems on the existence and uniqueness of solutions to the boundary value problems are proved. The results obtained in this paper cover the boundary value problems for one-dimensional differential equations with and without involution in the lower terms. |
| first_indexed | 2024-03-11T19:17:10Z |
| format | Article |
| id | doaj.art-783268842b2d418eb90737a6c2e69b13 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T19:17:10Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-783268842b2d418eb90737a6c2e69b132023-10-09T01:28:05ZengAIMS PressAIMS Mathematics2473-69882023-09-01811262752628910.3934/math.20231340Boundary value problems for a second-order differential equation with involution in the second derivative and their solvabilityAbdissalam Sarsenbi 0Abdizhahan Sarsenbi11. Research Center of Theoretical and Applied Mathematics, Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent, Kazakhstan 2. Department of Mathematics and Informatics, Tashenev University, Shymkent, Kazakhstan1. Research Center of Theoretical and Applied Mathematics, Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent, KazakhstanWe consider the two-point boundary value problems for a nonlinear one-dimensional second-order differential equation with involution in the second derivative and in lower terms. The questions of existence and uniqueness of the classical solution of two-point boundary value problems are studied. The definition of the Green's function is generalized for the case of boundary value problems for the second-order linear differential equation with involution, indicating the points of discontinuities and the magnitude of discontinuities of the first derivative. Uniform estimates for the Green's function of the linear part of boundary value problems are established. Using the contraction mapping principle and the Schauder fixed point theorem, theorems on the existence and uniqueness of solutions to the boundary value problems are proved. The results obtained in this paper cover the boundary value problems for one-dimensional differential equations with and without involution in the lower terms.https://www.aimspress.com/article/doi/10.3934/math.20231340?viewType=HTMLsecond-order differential equation with involutiongreen's functionnonlinear equationboundary value problemschauder fixed point theorem |
| spellingShingle | Abdissalam Sarsenbi Abdizhahan Sarsenbi Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability AIMS Mathematics second-order differential equation with involution green's function nonlinear equation boundary value problem schauder fixed point theorem |
| title | Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability |
| title_full | Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability |
| title_fullStr | Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability |
| title_full_unstemmed | Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability |
| title_short | Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability |
| title_sort | boundary value problems for a second order differential equation with involution in the second derivative and their solvability |
| topic | second-order differential equation with involution green's function nonlinear equation boundary value problem schauder fixed point theorem |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231340?viewType=HTML |
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