Multiple positive solutions for a higher order boundary value problem on time scales

Abstract

In this paper, we consider a nonlinear higher order three-point boundary value problem on time scales. We establish the criteria for the existence of one or two positive solutions for a higher order boundary value problem on time scales by using a result from the theory of fixed point index. Later, Leggett-Williams fixed-point theorem is used to investigate the existence of at least three positive solutions for a higher order boundary value problem on time scales. As an application, to demonstrate our results we also give an example. © 2016, House of the Book of Science. All rights reserved.