Multiple positive solutions for some p-Laplacian boundary value problems

This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian(ϕp(x′(t)))′+q(t)f(t,x(t),x′(t))=0,t∈(0,1)subject to the following boundary value conditions:x(0)=∑i=1nαix(ξi),x(1)=∑i=1nβix(ξi),where ϕp(s) = ∣s∣p−2 · s, p > 1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem.