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In this paper the author considered the existence of solutions of second-order Hamiltonian systems.I find some new existence results of nontrivial solutions for generalized asymptotically linear Hamiltonian systems. Some multiplicity results are established also. The methods used here were based on combining the Morse index and the critical group at an isolated critical point and the critical group at infinity. The main results are theorem 1,2,3.
Keywords:Nontrivial solution ; Morse index ; Critical group