Turkish Journal of Mathematics
Abstract
In this study, it is aimed to examine the solutions of the following nonlocal boundary value problem \begin{equation*} y^{(4)}+g(x,y)=0,x\in [{c,d}], y(c)=y'(c)=y''(c)=0,y(d)=\lambda y(\xi). \end{equation*} Here, $\xi\in ({c,d}),\lambda \in \mathbb{R},g\in C([{c,d}]\times \mathbb{R},\mathbb{R})$ and $g(x,0)\neq 0.$ It is concentrated on applications of Green's function that corresponds to the above problem to derive existence and uniqueness results for the solutions. One example is also given to demonstrate the results.
DOI
10.3906/mat-2007-79
Keywords
Nonlocal boundary value problems, Green's function, existence and uniqueness of solutions
First Page
1941
Last Page
1949
Recommended Citation
ERTÜRK, VEDAT SUAT
(2020)
"A unique solution to a fourth-order three-point boundary value problem,"
Turkish Journal of Mathematics: Vol. 44:
No.
5, Article 31.
https://doi.org/10.3906/mat-2007-79
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss5/31
