Abstract.
We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in \({\Bbb R}^N\) of the form \(\ddot q=q-W'(t,q)\), where we assume the existence of a sequence \((t_n)\subset{\Bbb R}\) such that \(t_n\to \pm\infty\) and \(W'(t+t_n,x)\to W'(t,x)\) as \(n\to\pm\infty\) for any \((t,x)\in{\Bbb R}\times{\Bbb R}^N\). Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions.
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Received February 2, 1996 / In revised form July 5, 1996 / Accepted October 10, 1996
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Montecchiari, P., Nolasco, M. & Terracini, S. Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems. Calc Var 5, 523–555 (1997). https://doi.org/10.1007/s005260050078
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DOI: https://doi.org/10.1007/s005260050078