Homoclinic Orbits for a Quasi-Linear Hamiltonian System

The aim of this paper is to prove existence of nontrivial homoclinic orbits for the following Quasilinear Hamiltonian System (a(|u′|p)|u′|p−2u′)′ − b(|u|p)|u|p−2u + W′u(t, u) = 0 in R that is, to prove existence of u : R → Rn satisfying the system above and u(−∞) =u′(−∞) = u(+∞) = u′(+∞) = 0.