Existence Of Solutions Of Several Kinds Of Difference Equations

In this paper,we mainly study the existence of solutions for the fractional order discrete La place equation,first order discrete Hamiltonian system and discrete nonlinear Schr(?)dinger equa tion using critical point theory.In Chapter 2,the fractional order discrete Laplace equation of the following form is studied:Where s ∈(0,1),V:Z→(0,∞),f:Z × R→R is a continuous function.Considering the nonlinear terms in the superlinear and sublinear cases,the existence of homoclinic solutions of the equation is proved using the mountain pass theorem and bounded theorem below.In Chapter 3,discrete nonlinear Schr(?)dinger equation of the following form is studied:When the potential function has periodicity,the existence of the ground state solution of the di screte nonlinear Schr(?)dinger equation is proved.Our conditions can be used to improve the resu lts of the continuous nonlinear Schr(?)dinger equation.In Chapter 4,the first order discrete Hamiltonian systems of the following form is studied:The existence of the minimum energy solution of the system when H(n,z)=1/2S(n)z·z+R(n,z)satisfies the period condition and when R(n,z)is superl inear at 0 and superquadratic at infinity is studied mainly by using the critical points theory of strongly indefinite general functions.