Existence and iteration of positive solutions to a class of Sturm–Liouville-like pp-Laplacian boundary value problems

This paper deals with the existence and iteration of positive solutions for the following pp-Laplacian differential equation: View the MathML source(ϕp(u′(t)))′+q(t)f(t,u(t),u′(t))=0,t∈(0,1), Turn MathJax on subject to the following Sturm–Liouville-like four-point boundary condition: View the MathML sourceu(0)−αu′(ξ)=0,u(1)+βu′(η)=0 Turn MathJax on where ξ,η∈(0,1)ξ,η∈(0,1). By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.