We are concerned with the solvability of the fourth-order four-point
boundary value problem
$$
\begin{cases}
u^{(4)}(t)=f(t,u(t),u^{\prime\prime}(t)),\quad t\in[0,1],\\
u(0)=u(1)=0,\\
au''(\zeta_1)-bu'''(\zeta_1)=0,\quad cu''(\zeta_2)+du'''(\zeta_2)=0,\end{cases}
$$
where $0\leq \zeta_1\zeta_2\leq 1$, $f\in C([0,1]\times
[0, \infty)\times (-\infty,0],[0, \infty))$. By using Guo–Krasnosel'skiĭ's
fixed point theorem on cones,
some criteria are established to ensure the existence, nonexistence and multiplicity
of positive solutions for this problem.
Keywords:
concerned solvability fourth order four point boundary value problem begin cases t prime prime quad zeta bu zeta quad zeta zeta end cases where leq zeta zeta leq times infty times infty infty using guo krasnoselski fixed point theorem cones criteria established ensure existence nonexistence multiplicity positive solutions problem
Affiliations des auteurs :
Yuqiang Feng
1
;
Xincheng Ding
1
1
School of Science Wuhan University of Science and Technology Wuhan 430065, P.R. China
@article{10_4064_ap104_1_2,
author = {Yuqiang Feng and Xincheng Ding},
title = {On the solvability of a fourth-order
multi-point boundary value problem},
journal = {Annales Polonici Mathematici},
pages = {13--22},
year = {2012},
volume = {104},
number = {1},
doi = {10.4064/ap104-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap104-1-2/}
}
TY - JOUR
AU - Yuqiang Feng
AU - Xincheng Ding
TI - On the solvability of a fourth-order
multi-point boundary value problem
JO - Annales Polonici Mathematici
PY - 2012
SP - 13
EP - 22
VL - 104
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/ap104-1-2/
DO - 10.4064/ap104-1-2
LA - en
ID - 10_4064_ap104_1_2
ER -
%0 Journal Article
%A Yuqiang Feng
%A Xincheng Ding
%T On the solvability of a fourth-order
multi-point boundary value problem
%J Annales Polonici Mathematici
%D 2012
%P 13-22
%V 104
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap104-1-2/
%R 10.4064/ap104-1-2
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%F 10_4064_ap104_1_2
Yuqiang Feng; Xincheng Ding. On the solvability of a fourth-order
multi-point boundary value problem. Annales Polonici Mathematici, Tome 104 (2012) no. 1, pp. 13-22. doi: 10.4064/ap104-1-2
