Nontrivial Solutions of Superquadratic Hamiltonian systems with Lagrangian Boundary Conditions and the L-index Theory

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems (t) = J▽H(t, z(t)) with Lagrangian boundary conditions, where is a semipositive symmetric continuous matrix and satisfies a superquadratic condition at infinity. We also obtain a result about the L-index. Partially supported by the National Natural Science Foundation of China (Nos. 10531050, 10621101) and the 973 Project of the Ministry of Science and Technology of China.