Existence and iteration of positive solutions for some pp-Laplacian boundary value problems

This paper deals with the existence and iteration of positive solutions for the following pp-Laplacian differential equation, (ϕp(u′(t)))′+q(t)f(t,u(t),u′(t))=0,t∈(0,1), subject to one of the following boundary conditions, αϕp(u(0))−βϕp(u′(0))=0,γϕp(u(1))+δϕp(u′(1))=0, or u(0)−g1(u′(0))=0,u(1)+g2(u′(1))=0. The main tool is the monotone iterative technique. We obtain not only the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.