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

摘要

Infinitely many periodic 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 subouadratic, asymptotically quadratic and superquadratic at infinity, but the existence results are the same. Secondly, the global conditions (F(t, - x) = F(t, x), for all x is an element of R-N) and (F(t, x) = 0, for all x is an element of R-N) assumed previously by others can be replaced by the local conditions (F(t, x) = F(t, x), vertical bar x vertical bar = r) and (F(t, x) = 0, vertical bar x vertical bar = r). Several examples are given to illustrate the main result. (C) 2018 Elsevier Ltd. All rights reserved.