Existence Of Homoclinic Orbits For A Class Of First Order Discrete Hamiltonian Systems

As is known to all, the Hamilton system is used to describe the object movement orbit. What’s more, looking for the general various invariant to the solution of the Hamilton system, has become one of the problems that scholars concerned.In this paper we consider the first order discrete Hamiltonian systems Where W(n, z)=1/2Snz·z+H(n,z) is superlinear as|z|â†'∞. We prove the existence of homoclonic orbit of the system by critical point theory. This dissertation is divided into four chapters. The main contents are follows:In Chapter1, a brief introduction is given to the historical background, status and up-to-date progress for all the investigated programs together with main results.In Chapter2, we show a few basic concepts related to this thesis, the analysis of the several difficulties encountered in solving the problem, presents the corresponding variational framework.In Chapter3. we prove the existence of the minimum energy solution of the first order discrete Hamilton system (1) by critical point theory when W(n, z) depends pe-riodically on n.In Chapter4, we consider the problem (1) with asymptotically periodic nonlin- earities. and Gz(n, z) need not to be periodic in n.