Existence and Uniqueness of Solutions for a Third-Order Three-Point Boundary Value Problem via Measure of Noncompactness

Abstract

In this paper, we consider a nonlinear third-order three-point boundary value problem and give the existence and uniqueness of solutions by constructing Green’s function and using its properties. The methods used here are based on Darbo’s fixed point theorem combined with the technique of measure of noncompactness. Finally, as applications, two examples are given to illustrate our main results.