A periodic solution for a second-order asymptotically linear Hamiltonian system

摘要

We study the existence of a periodic solution of the following second-order Hamiltoniansystem: ü(t)+▽F(t, u(t)) = 0, t ∈[0,T ], where F(t, x) = —K(t, x) + W(t, x). Assuming that K satisfies the "pinching" conditionand W is asymptotically linear at infinity, the existence of a nontrivial periodic solution isobtained via the Mountain Pass Theorem.