Positive Solutions For Several Kinds Of Boundary Value Problems Of Dynamic Equations On Time Scales

The theory of time scales was introduced by Stefan Hilger in 1988.After that more and more scholars take an interest in dynamic equations on time scales.There are two reasons. From the theoretical point of view, the time scales analysis theory can build bridges between continuous and dispersion. From the application point of view, dynamic equations on time scales has important applications. For example, the activities of insect populations in the different seasons and resting can be described by the dynamic equations on time scales.This paper mainly discusses the existence of solutions for several kinds of boundary value problems of nonlinear dynamic equations on time scales by using the Krasnosel’skii fixed point theorem and Schauder fixed point theorem. There are three chapters in this paper.In Chapter 1, introduce issues arising from the historical background and main tasks of this article.In Chapter 2, introduce preliminary knowledge of this article.In Chapter 3, discuss the existence of positive solutions of the following sin-gular BVP This paper obtains existence of positive solution by using the Krasnosel’skii fixed point theorem.In Chapter 4, studies the existence of positive solution for a singular third-order m point BVP on time scalesThis paper obtains existence of positive solution by using Schauder fixed point theory.