Existence And Multiplicity Of Positive Solutions For Discrete Semipositone Problems

In this paper, the existence and multiplicity of positive solutions for several classes of nonlinear difference equations boundary value problems are investigated by using the Guo-Krasnosel'skii fixed point theorem.In Chapter 1, we briefly introduce historical background, recently development and the main content of the thesis.In Chapter 2, we focuses on semipositone discrete Dirichlet boundary value problems. Firstly, we consider the Dirichlet boundary value problem which the k ?(0, 4 sin~2 (?)), and ? is a positive parameter, the existence of positive solutions is established for the nonlinear term is bounded below and f??(0, ?]which f?= (?), the explicit open interval of parameter is also given.And then, in more general, when the nonlinear is allowed to be unbounded below, we consider some existence and multiplicity results of positive solutions are established by using the fixed point theorem.In Chapter 3, we consider the semipositone discrete boundary value problems with the Neumann boundary conditions. Similarly, some results of existence and multiplicity of positive solutions are established for two cases. The first one is that the nonlinear term is bounded below, and the second is unbounded below.Similar to Chapter 2 and 3, some results of positive solutions for the semipositone discrete Robin boundary value problems are established by using GuoKrasnosel'skii fixed point theorem in Chapter 4.