Existence Of Multiple Solutions To Second-order Nonlinear Discrete Boundary Value Problems

The existence of multiple solutions for nonlinear discrete boundary value problem has important theoretical significance and stronger practical value.By combining the invariant set of descending flow with variational method,we mainly deals with the existence of multiple solutions for several types of second-order discrete boundary value problems.The thesis is organized by four chapters as following.In chapter 1,we give a brief introduction to the historical background and the recent development of the problems to be studied.We also state the main results of our work.In chapter 2,when the nonlinear element satisfies asymptotically linear at ?,we establishes the corresponding variational functional and reduces the problem of finding multiple solutions of discrete boundary value problems to that of seeking critical points of the functional.Making use of the invariant set of descending flow,we obtained some results on the existence of multiple solutions for a class of second-order nonlinear discrete Dirichlet boundary value problem.Finally,we use relevant examples to verify the feasibility of the theorem.Similar to Chapter 2,we study a class of second-order nonlinear discrete Dirichlet boundary value problem with parameter dependence and establish some results on the existence of multiple solutions in Chapter 3.We also give an example to illustrate our main results.For a class of second-order nonlinear discrete Robin boundary value problem with parameter dependence,we establish the existence of multiple solutions which include positive solutions,negative solutions and sign-changing solutions in a similar way in Chapter 4.