Asymptotically linear Hamiltonian system

We investigate the multiplicity of solutions for the Hamiltonian system with some asymptotically linear conditions. We get a theorem which shows the existence of at least three 2π2π-periodic solutions for the asymptotically linear Hamiltonian system. We obtain this result by the variational reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory and the variational method.