Boundary Value Problems Of P-Laplacian Difference Equations

Two p-Laplacian difference equations with Dirichlet boundary value conditions are considered in this paper.By introducing a basic function space,establishing a suitable variational framework,and using the critical point theory,we obtained the existence of at least two nontrivial solutions of one problem and some sufficient conditions for the existence of at least two positive solutions of the other problem.The present paper is organized as follows:In chapter 1,we introduce a brief description of history and significance of the topics.Then we state the research status and what we mainly do in this paper.Besides,some relevant preparation knowledge is given.In chapter 2,we consider the existence of solutions for a class of boundary value problem for p-Laplacian difference equation containing both advance and retardation.Using the Mountain Pass Lemma,we obtain some sufficient conditions for the existence of nontrivial solutions.In addition,sublinear case is considered as well.And we also obtain some sufficient conditions for the existence of nonzero solutions.In chapter 3,we discuss the existence of positive solutions for a class of boundary value problem of p-Laplacian difference equation.We obtain some sufficient conditions that there are at least two positive solutions of the problem by using the critical point theory.