|
This article is cited in 2 scientific papers (total in 2 papers)
Scientific articles
On the existence and uniqueness of a positive solution to a boundary value problem for a nonlinear ordinary differential equation of even order
G. È. Abduragimov, P. E. Abduragimova, M. M. Kuramagomedova Daghestan State University
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.
Keywords:
boundary value problem, positive solution, existence, uniqueness.
Received: 07.08.2021
Citation:
G. È. Abduragimov, P. E. Abduragimova, M. M. Kuramagomedova, “On the existence and uniqueness of a positive solution to a boundary value problem for a nonlinear ordinary differential equation of even order”, Russian Universities Reports. Mathematics, 26:136 (2021), 341–347
Linking options:
https://www.mathnet.ru/eng/vtamu235 https://www.mathnet.ru/eng/vtamu/v26/i136/p341
|
Statistics & downloads: |
Abstract page: | 118 | Full-text PDF : | 64 | References: | 32 |
|