Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation

Abstract

We are concerned with perturbations of the Hamiltonian system of the type

$$\text{q-L(t)}{}_{\mathrm{q}}\text{+W}{}_{\mathrm{q}}\text{(t,q)=0, t ϵ}$$

$\text{R}$, where q = (q₁, … , q_N) ε $\text{R}$^N, W ϵ C¹ ($\text{R}$ × $\text{R}$^N, $\text{R}$), and L(t) ϵ C ($\text{R}$, $\text{R}$^N2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS).