EXISTENCE AND MULTIPLICITY OF HOMOCLINIC SOLUTIONS FOR DAMPED VIBRATION SYSTEMS WITH SUB-QUADRATIC POTENTIAL

Abstract

In this paper, the existence result for homoclinic solutions of damped vibration systems with sub-quadratic potential is obtained by linking theorem. The conditions in this case are simple and more relaxed. Especially, no symmetry and no AR type conditions imposed on the potential in proving the existence result are the novelties in the paper. Recent results in the literature are generalized and significantly improved.