DefinePK

Abstract

In this paper we are concerned with the following damped vibration problem where ,  with  and ,  is -periodic in  such that  is a -periodic, positive definite symmetric matrix and  satisfies the global Ambrosetti-Rabinowitz condition or is subquadratic at infinity. By use of the Mountain Pass Theorem or the genus properties in the critical theory, we establish some new criteria to guarantee the existence and multiplicity of periodic solutions. Recent results in the literature are generalized and significantly improved.