On the solvability of a fourth-order multi-point boundary value problem

Yuqiang Feng¹ ; Xincheng Ding¹

¹ School of Science Wuhan University of Science and Technology Wuhan 430065, P.R. China

Annales Polonici Mathematici, Tome 104 (2012) no. 1, pp. 13-22.

Résumé

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.

Détail

DOI : 10.4064/ap104-1-2

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