Positive solutions to a boundary value problem for one nonlinear ordinary differential equation of even order
UDC
517.927.4EDN
AKVEYADOI:
10.31429/vestnik-22-1-6-13Abstract
The boundary value problem is considered
\begin{align*}
&x^{(2n)}(t)+f(t,x(t))=0,\qquad 0<t<1,\\
&x(0)=x'(0)=\dots=x^{(2n-2)}(0)=0, \\
&x(1)=0,
\end{align*}
where $n\in N$, the function $f(t,u)$ is non-negative and continuous on $[0, 1]\times [0,\infty)$, and $f(\,\cdot\,, 0)\equiv0$.
Using Krasnoselsky's theorem on fixed points in a cone, sufficient conditions for the existence of at least one positive solution to the problem under consideration are obtained. Examples are given to illustrate the results obtained.
Keywords:
differential equation, positive solution, boundary value problem, cone, Green's functionFunding information
The study did not have sponsorship.
References
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Dates
Submitted
February 18, 2025
Accepted
March 10, 2025
Published
March 27, 2025
How to Cite
[1]
Abduragimov, G.E., Positive solutions to a boundary value problem for one nonlinear ordinary differential equation of even order. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2025, т. 22, № 1, pp. 6–13. DOI: 10.31429/vestnik-22-1-6-13
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Copyright (c) 2025 Абдурагимов Г.Э.
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