Positive solutions for singular three-point boundary-value problems

Abstract

In this paper, we present the Green's functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green's functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.

Keywords

• Green's function
• second-order three-point boundary value problem
• explicit solution
• iteration