Existence Of Periodic Solutions And Homosexual Solutions For Two Classes Of Hamiltonian Systems

The Hamilton system, at the beginning as a canonical form of classical mechanics, was given by Hamilton, W. R, the English mathematician, in 19 century. It is widely used in Physics, Biology and other subjects. With the help of the tool, people acquire great achievements; At the end of 19 century, the variational methods was found and especially after 1970s, the critical point theory is known and many scholars begin to study the exis-tence of solutions for Hamilton systems in mathematics. In recent years, mathematicians get a great many results in this field. In this paper, we apply the variational methods, the critical point theory and other tools to prove the existence of at least one periodic solution and infinitely many homoclinic orbits for two kinds of Hamilton systems.This paper is divided into two chapters:Chapter 1 By using of the local linking theorem, we get the existence of at least one periodic solution for the system: which has more generalized condition.Chapter 2 We apply a generalized linking theorem to prove the existence of infinitely many homoclinic orbits for the system: under the weaker superlinear condition.