Investigations On Periodic And Subharmonic Solutions Of A Particular Kind Of Super-quadratic Hamiltonian Systems

This paper considers first-order non-autonomous Hamiltonian systems with new super-quadratic conditions covering the case where,??^> 1,?,v> 0 with Using an improved version of the generalised Mountain Pass Theorem, we obtain the existence of periodic solutions. Based on the existence theorem, we find out infinitely many distinct subharmonic solu-tions. Finally, by means of a critical point theorem for even functionals, we obtain an unbounded sequence of periodic solutions.This paper is divided into five parts. The 1st chapter briefly introduces the back-ground knowledge for Hamiltonian systems, summarize the research fruits in this field, puts forward our research issue and points out where we generalizes the work done before. The 2nd chapter provides the functional space needed in this paper, gives the embedding theorem and two critical point theorems. The 3rd chapter proves the exis-tence results of periodic solutions of Hamiltonian systems. The 4th chapter proves the multiplicity results of subharmonic solutions of Hamiltonian systems. The 5th chapter proves the multiplicity result of periodic solutions of Hamiltonian systems.