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Multiple Homoclinic Solutions for Second-Order Perturbed Hamiltonian Systems

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Abstract

In this paper, we study the second-order perturbed Hamiltonian systems

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where inline image is a parameter, inline image is positive definite for all inline image but unnecessarily uniformly positive definite for inline image, and W is either asymptotically quadratic or superquadratic in x as inline image. Based on variational methods, we prove the existence of at least two nontrivial homoclinic solutions for the above system when inline image small enough.

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