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

We study the existence of a periodic solution of the following second-order Hamiltonian system: ü(t)+∇F(t,u(t))=0,t∈[0,T], where F(t,x)=−K(t,x)+W(t,x)F(t,x)=−K(t,x)+W(t,x). Assuming that KK satisfies the “pinching” condition and WW is asymptotically linear at infinity, the existence of a nontrivial periodic solution is obtained via the Mountain Pass Theorem.