Existence And Multiplicity Of Solutions For Second-order P-Laplacian Difference Systems With Parameters

In this paper, we mainly study existence and multiplicity of solutions for second-order nonlinear p-Laplacian difference systems with parameters by using the critical point theory and the minimax principle. The structure of this paper as follows:In the first chapter, we introduce the background of the discussed problem of this thesis briefly, and we give the main results of this thesis and the discrete variational structure.In the second chapter, by using the critical point theory and the minimax principle, we investigate existence of solutions for second-order nonlinear p-Laplacian difference systems with one parameter as follows: which are resonant at an arbitrary eigenvalue.In the third chapter, by using the three critical points theory, we investigate mul-tiplicity of solutions for second-order nonlinear p-Laplacian difference systems with two parameters as follows: Here,φ(s)=|s|p-2s(p>1),T>2is a given positive integer,Z[1,T]denotes the discrete interval{1,2,...,T},G∈C1(Z[1,T]×R2,R+),F∈C1(Z[1,T]×R2,R), Gt、Gs、Ft、Fs are the partial derivatives of G and F for their second and third variables respectively,△is the forward difference operator,i.e.△u(i)=u(i+1)-u(i),△2u(i)=△(△u(i)).