Bounded solutions to a three-point fourth-order iterative boundary value problem

Abstract

The aim of this paper is to deal with a fourth-order three-point boundary value problem with an iterative source term. By using a technique based on Green’s function method, the contraction mapping principle and Schauder’s fixed point theorem, we establish some sufficient conditions for proving the existence, uniqueness and continuous dependence of a bounded solution on parameters. Furthermore, two examples are provided to illustrate the main findings, which are completely new, and extend some relevant works to some degree.