Email this article On the existence and uniqueness of a positive solution to a boundary value problem for a nonlinear ordinary differential equation of even order
- Authors: Abduragimov G.E.1, Abduragimova P.E.1, Kuramagomedova M.M.1
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Affiliations:
- Dagestan State University
- Issue: Vol 26, No 136 (2021)
- Pages: 341-347
- Section: Original articles
- URL: https://journals.rcsi.science/2686-9667/article/view/296463
- ID: 296463
Cite item
Abstract
In the article, we consider a boundary value problem for a nonlinear ordinary differential equation of even order which, obviously, has a trivial solution. Sufficient conditions for the existence and uniqueness of a positive solution to this problem are obtained. With the help of linear transformations of T. Y. Na [T. Y. Na, Computational Methods in Engineering Boundary Value Problems, Acad. Press, NY, 1979, ch. 7], the boundary value problem is reduced to the Cauchy problem, the initial conditions of which make it possible to uniquely determine the transformation parameter. It is shown that the transformations of T. Y. Na uniquely determine the solution of the original problem. In addition, based on the proof of the uniqueness of a positive solution to the boundary value problem, a sufficiently effective non–iterative numerical algorithm for constructing such a solution is obtained. A corresponding example is given.
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About the authors
Gusen E. Abduragimov
Dagestan State University
Author for correspondence.
Email: gusen_e@mail.ru
ORCID iD: 0000-0001-7095-932X
Candidate of Physics and Mathematics, Associate Professor of the Applied Mathematics Department
Russian Federation, 33 M. Hajiyev St., Makhachkala 367025, Russian FederationPatimat E. Abduragimova
Dagestan State University
Email: abpatuka@mail.ru
ORCID iD: 0000-0001-9050-0209
Post-Graduate Student, Applied Mathematics Department
Russian Federation, 33 M. Hajiyev St., Makhachkala 367025, Russian FederationMadina M. Kuramagomedova
Dagestan State University
Email: madina19.12@mail.ru
ORCID iD: 0000-0001-6424-9348
Post-Graduate Student, Applied Mathematics Department
Russian Federation, 33 M. Hajiyev St., Makhachkala 367025, Russian FederationReferences
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