Existence of multiple positive solutions for Sturm–Liouville-like four-point boundary value problem with image-Laplacian Original Research Article

In this paper, we consider the Sturm–Liouville-like four-point boundary value problem with pp-Laplacian View the MathML source(ϕp(u′))′(t)+f(t,u(t))=0,t∈(0,1), Turn MathJax on View the MathML sourceu(0)−αu′(ξ)=0,u(1)+βu′(η)=0, Turn MathJax on where ϕp(s)=|s|p−2s,p>1ϕp(s)=|s|p−2s,p>1. By means of a fixed-point theorem for operators on a cone, the existence of multiple (at least three) positive solutions to the above boundary value problem is obtained.