Minimax Critical Point Theory And Its Application In The Hamiltonian System,

This paper considers the Mountain Pass theorem which is one of the most important theorems in minimax theory. We generalize it into operator form from functional form. Then we apply some generalized forms of Mountain Pass theorem to the Hamiltonian systems q + Aq + V'(q}=0. The research work about Hamiltonian systems at present mostly consider the case A = O.We assume that the term of linearity is a invariable matrix and the Potential satisfies superquadratic nonhomogenus conditions. Under this assumption, we prove that the systems possess periodic solutions with prescribe period.