On the existence and uniqueness of a positive solution to a boundary value problem for one nonlinear functional differential equation of third order
UDC
517.927.4DOI:
https://doi.org/10.31429/vestnik-21-2-6-13Abstract
The boundary value problem is considered
$x'''(t)+f \left (t,\left(Tx \right)(t) \right)=0,\quad 0<t<1,$
$x(0)=x(1)=0,$
$x''(0)=x''(1),$
where $T$ — linear positive continuous operator.
Using the Green's function and Krasnoselsky's fixed point theorem, we formulate and prove the existence of positive solutions to the above boundary value problem for a third-order nonlinear functional differential equation. Next, in the sublinear case, using the fixed point principle, we establish the uniqueness of a positive solution to the problem under study. In addition, an example is given to illustrate the results obtained.
Keywords:
positive solution, boundary value problem, cone, Green's functionAcknowledgement
The study did not have sponsorship.
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Submitted
2024-03-26
Published
2024-06-28
How to Cite
Abduragimov G.E.
On the existence and uniqueness of a positive solution to a boundary value problem for one nonlinear functional differential equation of third order.
Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation,
2024,
vol. 21,
no. 2,
pp. 6-13.
DOI: https://doi.org/10.31429/vestnik-21-2-6-13
(In Russian)
Copyright (c) 2024 Abduragimov G.E.
This work is licensed under a Creative Commons Attribution 4.0 International License.
