Existence of solution for a nonlinear three-point boundary value problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1120-1134
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In this paper, we study the existence of
nontrivial solution for the fourth-order three-point boundary value
problem given as follows
\begin{gather*}
u^{(4)}(t)+f(t,u(t))=0,\quad\text 01,\\
u^{'}(0)-\alpha u^{'}(\eta)=0,\quad u(0)=u^{'''}(0)=0,\quad
u^{'}(1)-\beta u^{'}(\eta)=0,
\end{gather*}
where $\eta\in(0,1)$, $\alpha, \beta\in\mathbb{R}$, $f\in
C([0,1]\times\mathbb{R},\mathbb{R})$. We give sufficient conditions
that allow us to obtain the existence of a nontrivial solution. And
by using the Leray–Schauder nonlinear alternative we prove the
existence of at least one solution of the posed problem. As an
application, we also given some examples to illustrate the results
obtained.
Keywords:
Green's function, Nontrivial solution, Leary-Schauder nonlinear alternative, Fixed point theorem, Boundary value problem.
@article{SEMR_2017_14_a98,
author = {Z. Bekri and S. Benaicha},
title = {Existence of solution for a nonlinear three-point boundary value problem},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {1120--1134},
publisher = {mathdoc},
volume = {14},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a98/}
}
TY - JOUR AU - Z. Bekri AU - S. Benaicha TI - Existence of solution for a nonlinear three-point boundary value problem JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2017 SP - 1120 EP - 1134 VL - 14 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a98/ LA - en ID - SEMR_2017_14_a98 ER -
Z. Bekri; S. Benaicha. Existence of solution for a nonlinear three-point boundary value problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1120-1134. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a98/