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Abstract The existence of homoclinic solutions for the non-periodic second order Hamiltonian systems was studied. Under a class of new superquadratic conditions, a new existence result was obtained by applying the Mountain Pass Theorem relying on Ekeland’s variational principle, the spectral theory of self-adjoint operators and finite dimensional approximations. The recent results in the literature were generalized and significantly improved.
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Received: 09 January 2018
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2017, Vol. 30 
