Non-periodic damped vibration systems with sublinear terms at infinity: Infinitely many homoclinic orbits

In this paper, we study a class of non-periodic damped vibration systems with subquadratic terms. We obtain infinitely many nontrivial homoclinic orbits by a variant fountain theorem developed recently by Zou. To the best of our knowledge, there is no result published concerning the existence of infinitely many homoclinic orbits for this class of non-periodic damped vibration systems with subquadratic terms at infinity.