Existence And Multiplicity Of Periodic Solutions For Second Order Hamiltonian Systems

This thesis studies the existence of periodic solutions for second order Hamiltonian systems based on the local linking theorem, mountain pass theorem, minimax methods and so on. And we obtain several new results.The thesis is divided into five sections according to the contents.Chapter 1 briefly introduces the researched background of problems and the main work of the paper.Chapter 2 studies the existence of periodic solutions for second order non-autonomous Hamiltonian systems x(t)-B(t)x(t)+â–½H(t,x(t))=0, under local superquadratic condition. We obtain several new existence theorems by mountain pass theorem and local linking theorem, which improve previously known results.Chapter 3 studies the existence of subharmonic solutions for second order non-autonomous Hamiltonian systems u(t)+â–½F(t,u(t))=0, under more general conditions. We obtain several new existence theorems by Saddle point theorem.Chapter 4 studies the periodic solutions for second order non-autonomous Hamil-tonian systems with a change sign potential u(t)+â–½F(t,u(t))=0. We obtain the sufficient conditions of the existence of infinite many periodic solutions.Chapter 5 studies the existence and multiplicity of periodic solutions for Hamil-tonian systems with p-Laplacian by using the minimax methods. The obtained new results extend and improve two theorems of Ye and Tang...