Existence of positive solutions for a nonlinear fourth order boundary value problem
Volume 81 / 2003
Annales Polonici Mathematici 81 (2003), 79-84
MSC: Primary 34B18.
DOI: 10.4064/ap81-1-7
Abstract
We study the existence of positive solutions of the nonlinear fourth order problem $$ \eqalign{ &u^{(4)}(x)=\lambda a(x)f(u(x)),\cr &u(0)=u'(0)=u' '(1)=u' ' '(1)=0,\cr}$$ where $a: [0,1]\rightarrow \mathbb R$ may change sign, $f(0)>0$, and $\lambda>0$ is sufficiently small. Our approach is based on the Leray–Schauder fixed point theorem.
