Multiple And Sign-changing Solutions For Boundary Value Problems Of Second-order Nonlinear Difference Equations

With the development of science and technology, the difference equation the-ory is extensively applied in many fields, such as information system, population ecology, modern physics, engineering control and so on. Studying the existence of solutions for boundary value problems of second-order nonlinear difference equa-tions is an important research direction in the area of difference equation, it also has great theoretical significance and strong practical value. Using the method of invariant sets of descending flow, we mainly deal with the existence of multiple and sign-changing solutions for boundary value problems of two types of second-order nonlinear difference equations in this thesis.This thesis is divided into three chapters. Main contents are as follows.In chapter one, we give a brief introduction to the historical background and mention our main results of our work. At the end of this part, we introduce some elementary concepts and fundamental lemmas which are related to our results.In chapter two, we focus on the existence of multiple and sign-changing so-lutions for Neumann boundary value problem of a class of second-order nonlinear difference equations. By making use of the method of invariant sets of descending flow in combination with variational method, we establish sufficient conditions to obtain the existence of positive solutions, negative solutions and sign-changing so-lutions. In addition,an example is given to verify the practical effectiveness of our main theorem at length.Similar to chapter two, the existence of multiple and sign-changing solutions for a class of second-order nonlinear difference equations with Robin boundary condition are concerned in the third chapter. Finally, we also use the relevant example to verify the feasibility of the theorem.