Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems

We study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian system [email protected]?(t)[email protected]?[-K(t,u(t))+W(t,u(t))]=0. The existence of a nontrivial periodic solution is obtained when @?W is asymptotically linear at infinity, and the existence of infinitely many periodic solutions is also obtained when @?W is superlinear.

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