Higher order nonlinear dynamic systems on time scales

Abstract

In this paper, we consider a nonlinear system of higher order three-point boundary value problems on time scales. The Schauder fixed point theorem is used to investigate the existence of solutions of nonlinear dynamic systems on time scales. Furthermore, we establish the criteria for the existence of at least one, two and three positive solutions for higher order nonlinear dynamic systems on time scales by using the four functionals fixed point theorem, the Avery–Henderson fixed point theorem and the five functionals fixed point theorem, respectively.