Subharmonic Solutions Of Non-autonomous Hamiltonian Systems With (q,p)-Laplacian

In this thesis,we deal with the subharmonic solutions of non-autonomous Hamiltonian systems with (q,p)-Laplacian by using variational method. The thesis consists of three chapters.Chapter 1 is the introduction and the main results of this thesis are also given.In chapter 2, we introduce some preliminaries which will be used.In chapter 3, using the saddle point theorem, we concern with the following non-autonomous Hamiltonian systems with (q,p) -Laplacian:where 1<q,/p<+∞, F:R×RN×RN→R is T-periodic in its first variable with T > 0. Introducing some kinds of control functions, we establish the existence of subharmonic solutions for the above mentioned problem. Our theorems generalize and improve several known results in the literature.