Existence and iteration of positive solutions for some image-Laplacian boundary value problems Original Research Article

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 one of the following boundary conditions, View the MathML sourceαϕp(u(0))−βϕp(u′(0))=0,γϕp(u(1))+δϕp(u′(1))=0, Turn MathJax on or View the MathML sourceu(0)−g1(u′(0))=0,u(1)+g2(u′(1))=0. Turn MathJax on 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.