The existence of symmetric positive solutions for Sturm-Liouville-like four-point boundary value problem with a p-Laplacian operator

In this paper, the Sturm-Liouville-like four-point boundary value problem with a p-Laplacian operator(ϕp(u′))′(t)+λa(t)f(t,u(t))=0,t∈(0,1),u(0)-αu′(ξ)=0,u(1)+αu′(η)=0is studied, where ϕp(s)=|s|p-2s,p>1. By the use of fixed point index theory, Leray-Schauder degree and upper and lower solution method, some existence, nonexistence and multiplicity results of symmetric positive solutions are acquired.