# American Institute of Mathematical Sciences

March  2021, 26(3): 1627-1652. doi: 10.3934/dcdsb.2020176

## Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems

 1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China 2 School of Mathematics and Statistics, Xinyang Normal University, Henan 464000, China

* Corresponding author: Chun-Lei Tang

Received  January 2019 Revised  March 2020 Published  March 2021 Early access  June 2020

Fund Project: The first author is supported by Fundamental Research Funds for the Central Universities (XDJK2020B051) and National Natural Science Foundation of China(No. 11601438, 11971393)

In this paper, we consider a class of second-order Hamiltonian systems of the form
 $\ddot{u}(t)-L(t) u(t)+\nabla W(t,u(t)) = 0$
where
 $L:R\rightarrow R^{N^2}$
and
 $W \in C^1(R\times R^N, R)$
are asymptotically periodic in
 $t$
at infinity. Under the reformative perturbation conditions and weaker superquadratic conditions on the nonlinearity, the existence of a ground state homoclinic orbit is established. The main tools employed here are the local mountain pass theorem and the concentration-compactness principle.
Citation: Ying Lv, Yan-Fang Xue, Chun-Lei Tang. Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1627-1652. doi: 10.3934/dcdsb.2020176
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