Existence and concentration of homoclinic orbits for first order Hamiltonian systems

Abstract

<abstract><p>This paper is concerned with the following first-order Hamiltonian system</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} \nonumber \dot{z} = \mathscr{J}H_{z}(t, z), \end{equation} $\end{document} </tex-math></disp-formula></p> <p>where the Hamiltonian function $ H(t, z) = \frac{1}{2}Lz\cdot z+A(\epsilon t)G(|z|) $ and $ \epsilon > 0 $ is a small parameter. Under some natural conditions, we obtain a new existence result for ground state homoclinic orbits by applying variational methods. Moreover, the concentration behavior and exponential decay of these ground state homoclinic orbits are also investigated.</p></abstract>