Periodic Solutions For Second Order Hamiltonian Systems With Obstacles

The main purpose of this dissertation is to study the existence of periodic solutions for the following second order Hamiltonian systems:satisfying the following conditions:Since in some conditions, the above systems are equivalent to the following systems:So, in this dissertation, we obtain some existence theorems of problem (1.1) satisfying (1.2) and (1.3) by researching the periodic solutions of systems (I) or (II) via some new critical points theorem of locally Lipschitz functions.