Ground State Homoclinic Orbits for First-Order Hamiltonian System

  • Wen Zhang
  • Jian ZhangEmail author
  • Xianhua Tang


In this paper, we study the following first-order Hamiltonian system
$$\begin{aligned} \dot{z}=\mathscr {J}H_{z}(t,z). \end{aligned}$$
Under some suitable conditions on the nonlinearity, we establish the existence of ground state homoclinic orbits by using variational methods. Moreover, we also explore some properties of these homoclinic orbits, such as compactness of set of and exponential decay of ground state homoclinic orbits.


Hamiltonian system Ground state homoclinic orbits Exponential decay Variational methods 

Mathematics Subject Classification

37J45 70H05 



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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHunan University of CommerceChangshaPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsCentral South UniversityChangshaPeople’s Republic of China

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