Existence of periodic solutions for a class of damped vibration problems

摘要

In this paper, we are concerned with the existence of periodic solutions for a class of damped vibration problems. By introducing some new kinds of superquadratic and asymptotically quadratic conditions, and making use of the generalized mountain pass theorem in critical point theory, we propose a unified approach when the potential functionF(t,x)exhibits either an asymptotically quadratic or a superquadratic behavior at infinity, and establish some sufficient conditions on periodic solutions, which extend and improve some recent results in the literature, even without damped vibration term.