Existence and concentration of homoclinic orbits for first order Hamiltonian systems

Abstract

This paper is concerned with the following first-order Hamiltonian system $ \begin{equation} \nonumber \dot{z} = \mathscr{J}H_{z}(t, z), \end{equation} $ 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.

Keywords

• hamiltonian system
• ground state homoclinic orbits
• concentration