Damped vibration problems with sign-changing nonlinearities: infinitely many periodic solutions

Abstract

Abstract We obtain infinitely many nontrivial periodic solutions for a class of damped vibration problems, where nonlinearities are superlinear at infinity and primitive functions of nonlinearities are allowed to be sign-changing. By using some weaker conditions, our results extend and improve some existing results in the literature. Besides, some examples are given to illuminate our results.

Keywords

• damped vibration problems
• infinitely many periodic solutions
• sign-changing
• variational method