In this article, we consider a nonlinear higher-order

Abstract. In this paper, we consider the nonlinear even-order m-point boundary value problems on time scales. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point boundary value problems on time scales by using Krasnosel'skii's fixed point theorem and Leggett-Williams' fixed point theorem, respectively.

Abstract. In this paper, we establish the criteria for the existence of at least one and three positive solutions for a nonlinear second order multi-point time scale boundary value problem on infinite interval based on the LeraySchauder fixed point theorem and the five functional fixed point theorem, respectively.

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.