Multiple symmetric positive solutions to a new kind of four point boundary value problem

In this paper, we are concerned with the existence of multiple symmetric positive solutions for four point boundary value problems with one-dimensional pp-Laplacian (ϕp(x′(t)))′+h(t)f(t,x(t),x′(t))=0,01,ξ,η∈(0,1),ξ+η=1ϕp(s)=|s|p−2s,p>1,ξ,η∈(0,1),ξ+η=1. By using a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions. The interesting points here are that ξ>ηξ>η and the nonlinear term ff are involved with the first-order derivative explicitly.