The Existence Of Positive Solutions For Boundary Value Problems Of Difference Equations

Recent years, difference equations with boundary value conditions have been extensively studied by many authors. In this paper, we mainly investigate two classes of difference equations with boundary value conditions. We divide this article for four chapters. In chapter 1, we introduce the historical background of the problems and main works of this paper, definitions and properties we need in this paper are also given. Chapter 2 is devoted to studying the existence of solutions for nonlinear third order two-point difference equations with boundary value conditions by means of Krasnosel'skii fixed-point theorem. In chapter 3, applying fixed-point index theorem in cone, we study positive solutions for nonlinear second order three-point boundary value problem. Moreover, applying the same method in chapter 2, We mainly discuss the existence of solutions and multiple solutions for nonlinear second-order four-point boundary value problem in chapter 4.