On the solvability of a fourth-order multi-point boundary value problem
Volume 104 / 2012
Annales Polonici Mathematici 104 (2012), 13-22
MSC: Primary 34B10; Secondary 34B15.
DOI: 10.4064/ap104-1-2
Abstract
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.
