Well Ordered Monotone iterative Technique for nonlinear second order Four Point Dirichlet BVPs

Abstract

In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as, ... where ..., ... the non linear term ...is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution and upper solution such that... Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where