Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems

Ying Lv; Yan-Fang Xue; Chun-Lei Tang

doi:10.3934/cpaa.2019128

Article Contents

2019, Volume 18, Issue 5: 2855-2878. Doi: 10.3934/cpaa.2019128

This issue Previous Article A symmetry result for elliptic systems in punctured domains Next Article

Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author
^* Corresponding author

Received: September 30, 2017

Revised: March 31, 2018

Published: March 2019

Lv is supported by National Natural Science Foundation of China (No.11601438), Xue and Tang are supported by National Natural Science Foundation of China (No.11471267)

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Abstract

In this paper we consider the homoclinic orbits for a class of second order Hamiltonian systems of the form

$ \ddot{q}(t)-\lambda q(t)+\nabla W(t,q(t)) = 0 $

where $ \lambda>0 $ is a parameter, $ \frac{|\nabla W(t,x)|}{|x|} $ asymptotically tends to a constant as $ |x|\rightarrow\infty $ and $ |t|\rightarrow\infty $. Via the variational method, two new theorems are proved.

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Mathematics Subject Classification: Primary: 37J45, 37K05; Secondary: 58E05.

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