A Note on Homoclinic Orbits for Second Order Hamiltonian Systems
Bingyu Li, Fengying Li, Donglun Wu, Shiqing Zhang
TL;DR
This paper investigates the existence of homoclinic orbits in second order Hamiltonian systems using variational methods and Fourier analysis, providing new existence results under specific potential conditions.
Contribution
It introduces a novel application of the direct method of variations combined with Fourier analysis to establish homoclinic orbit existence in these systems.
Findings
Existence of homoclinic orbits proven under certain potential conditions
Application of variational methods to Hamiltonian systems
Use of Fourier analysis to support existence results
Abstract
In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential , we apply the direct method of variations and the Fourier analysis to prove the existence of homoclinc orbits.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems