Periodic Solutions for Damped Vibration Problems
Ziheng Zhang, Hongjun Li · Journal of Advances in Applied & Computational Mathematics · 2015
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.