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.
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
\Bibitem{AbdAbdKur21}
\by G.~\`E.~Abduragimov, P.~E.~Abduragimova, M.~M.~Kuramagomedova
\paper On the existence and uniqueness of a positive solution to a boundary value problem for a nonlinear ordinary differential equation of even order
\jour Russian Universities Reports. Mathematics
\yr 2021
\vol 26
\issue 136
\pages 341--347
\mathnet{http://mi.mathnet.ru/vtamu235}
\crossref{https://doi.org/10.20310/2686-9667-2021-26-136-341-347}
Linking options:
https://www.mathnet.ru/eng/vtamu235
https://www.mathnet.ru/eng/vtamu/v26/i136/p341
This publication is cited in the following 2 articles:
G. E. Abduragimov, “On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a 4nth-Order Nonlinear Ordinary Differential Equation”, Russ Math., 67:9 (2023), 16
G. È. Abduragimov, P. È Abduragimova, M. M. Kuramagomedova, “On the existence and uniqueness of a positive solution to a boundary-value problem of the Sturm–Liouville type for a nonlinear ordinary differential equation”, CMFD, 69:2 (2023), 201–207
Citation in format AMSBIB
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