| 摘要 | 第1-6页 |
| Abstract | 第6-7页 |
| 前言 | 第7-18页 |
| 1 Introduction of background and preliminary knowledge | 第18-28页 |
| ·Symplectic spaces | 第18-20页 |
| ·Symplectic diffeomorphisms and Hamiltonian vertor fields | 第20-22页 |
| ·Symplectic Capacities | 第22-23页 |
| ·The L-index theory | 第23-28页 |
| 2 Maslov-type index theory for symplectic paths with arbitrary Lagrangian boundary conditions | 第28-56页 |
| ·Introduction | 第28-33页 |
| ·The(L,L′)-index theory(i_L~(L′)(γ),v_L~(L′)(γ)) | 第29-30页 |
| ·Asymptotically Hamiltonian systems with Lagrangian boundary conditions | 第30-31页 |
| ·Brake solutions of asymptotically Hamiltonian systems | 第31-32页 |
| ·Sturm-Liouville problem | 第32-33页 |
| ·The(L,L′)-index theory | 第33-35页 |
| ·Galerkin approximation | 第35-38页 |
| ·The saddle point reduction | 第38-43页 |
| ·Applications | 第43-56页 |
| 3 Some abstract critical point theorems for self-adjoint operator equations and appli-cations | 第56-72页 |
| ·Introduction and main results | 第56-59页 |
| ·Proves of the main results | 第59-66页 |
| ·Applications | 第66-72页 |
| ·First order Hamiltonian systems | 第66-69页 |
| ·Second order Hamiltonian systems | 第69-72页 |
| 4 Symmetrical symplectic capacity with applications | 第72-98页 |
| ·Introduction and main results | 第72-74页 |
| ·Symmetrical symplectic capacity and its applications | 第74-94页 |
| ·Symmetrical symplectic capacity | 第74-88页 |
| ·Application to the existence of brake orbit | 第88-94页 |
| ·(N_0,S)-symmetrical symplectic capacity and applications | 第94-98页 |
| ·(N_0,S)-symmetrical symplectic capacity | 第94-95页 |
| ·Applications for S-symmetrical brake orbits | 第95-98页 |
| Bibliography | 第98-106页 |
| 致谢 | 第106-108页 |
| 个人简历与己完成的论文 | 第108页 |
