Existence and multiplicity of periodic solutions for damped vibration problems with nonlinearity of linear growth

摘要

In this paper, we study a class of damped vibration problems with nonlinearity of linear growth. We obtain the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and a critical point theorem. Compared with the existing work, our results do not require the system to be asymptotically linear at infinity. (C) 2020 Elsevier Ltd. All rights reserved.