Triple positive solutions for a second order m-point boundary value problem with a delayed argument

Abstract

In this paper, we establish the new expression and properties of Green’s function for an m-point boundary value problem with a delayed argument. Furthermore, using Hölder’s inequality and a fixed point theorem due to Leggett and Williams, the existence of at least three positive solutions is also given. We discuss our problem with a delayed argument. In this case, our results cover m-point boundary value problems without delayed arguments and are compared with some recent results. An example is included to illustrate our main results.