On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions

David G. Costa; Hossein Tehrani

On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions

Classical Analysis and ODEs 2012-11-30 v1 Analysis of PDEs

Authors: David G. Costa , Hossein Tehrani

Abstract

We show existence of infinitely many homoclinic orbits at the origin for a class of singular second-order Hamiltonian systems $\ddot{u} + V_u (t,u)=0\,,\quad -\infty < t < \infty\,.$ We use variational methods under the assumption that\ $V(t,u)$ \ satisfies the so-called "Strong-Force" condition.

Keywords

singular Hamiltonian systems homoclinic orbits variational methods strong-force condition second-order differential equations

Cite

@article{arxiv.1211.6779,
  title  = {On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions},
  author = {David G. Costa and Hossein Tehrani},
  journal= {arXiv preprint arXiv:1211.6779},
  year   = {2012}
}

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