Positive Solutions for a Nonlinear Three-point Boundary-value Problem

Abstract

We study the existence of positive solutions to the boundary-value problem $$ displaylines u''+a(t)f(u)=0,quad tin (0,1) cr u(0)=0,quadalpha u(eta)=u(1),, cr} $$ where $0<eta<1$ and $0<alpha<1/eta$. We show the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying the fixed point theorem in cones.