Existence of solutions of nonlinear m-point boundary-value problems

Abstract

We study the existence of positive solutions to the boundary-value problemu″+atfu=0,t∈0,1x′0=∑i=1m-2 bix′ξi,x1=∑i=1m-2aixξi,where ξi∈(0,1) with 0 <1, and ∑m-2i=1bi<1. 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. © 2001 Academic Press.