Nontrivial Solutions Of Asymptotically Linear N - Dimensional Indefinite Hamiltonian Systems

In this paper we will study the nontrivial solutions of asymptotically linear n dimensional indefinite Hamiltonian system: Px-V’(t, x)=0, (1) x(0)-x(1)=0=x(0)-x(1), (2) and Px-V’(t,x)= 0, (3) x(O)=0=x(1), (4)In chapter one, we recall some basic concepts and results in [11]. The knowledge is a basis of this paper. Meanwhile, we give some main results of this paper.In chapter two, we first discuss an index theory of the linear n dimensional indefinite Hamiltonian systems, then investigate the nontrivial periodic solutions for asymptotically linear n dimensional indefinite Hamiltonian systems. The main methods are the index theory of linear homogenous equations and some results of topological degree and variational methods. Then we get some main results such as the definitions 2.2-2.4 and the theories 2.1-2.2.In chapter three, we mainly discuss the nontrivial aperiodic solutions for asymp-totically linear n dimensional indefinite Hamiltonian systems with the similar meth-ods of chapter two. The main results of this chapter are the definitions 3.2-3.4 and the theories 3.1-3.2.