Positive solutions for a four-point boundary value problem with the pp-Laplacian

In this paper, we study the nonlinear four-point boundary value problem with the pp-Laplacian {(φp(u′))′+f(t,u(t))=0,01,α,β>0,0<ξ<η<1φp(s)=|s|p−2s,p>1,α,β>0,0<ξ<η<1. By applying a fixed point theorem in cones, sufficient conditions are given for the existence of a positive solution and multiple positive solutions. The interesting point is the Sturm–Liouville-like boundary condition, which was rarely treated until now.