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

2012/11/28 by David G. Costa, Costa, David G., Hossein Tehrani +1
Engineering · Mathematics · Physics and Astronomy · #34C25 #58E05 #58F05 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Control and Stability of Dynamical Systems #FOS: Mathematics #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #math.AP #math.CA #msc:34C25 #msc:58E05 #msc:58F05

paper · pdf · doi:10.48550/arxiv.1211.6779

arxiv created 2012/11/28 · openalex publication_date 2012/11/28 · arxiv updated 2012/11/30 · openalex created_date 2022/09/22 · openalex updated_date 2026/07/28

Abstract

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

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