Multiple periodic solutions for damped vibration systems with general nonlinearities at infinity

Abstract

Infinitely manyperiodic solutions for a class of damped vibration systems are obtained. We differ from previous results as follows. First, the nonlinearities are not restricted at infinity, i.e., they can be subquadratic, asymptotically quadratic and superquadratic at infinity, but the existence results are the same. Secondly, the global conditions (F(t,−x)=F(t,x), ∀x∈RN) and (F(t,x)≥0, ∀x∈RN) assumed previously by others can be replaced by the local conditions (F(t,−x)=F(t,x), |x|≤r) and (F(t,x)≥0, |x|≤r). Several examples are given to illustrate the main result.