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

We are concerned with perturbations of the Hamiltonian system of the type View the MathML source View the MathML source, where q = (q1, … , qN) ε View the MathML sourceN, W ϵ C1 (View the MathML source × View the MathML sourceN, View the MathML source), and L(t) ϵ C (View the MathML source, View the MathML sourceN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS).