Infinitely many fast homoclinic solutions for different classes of damped vibration systems

Abstract

. In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive definite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.