TITLE:
Multiple Periodic Solution for a Class of Damped Vibration System
AUTHORS:
Zihan Zhang, Yuanhao Wang, Guanggang Liu
KEYWORDS:
Damped Vibration Problems, Morse Theory, Critical Group, Morse Index, Minimization Method
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.12,
December
31,
2024
ABSTRACT: In this paper, we consider a class of damped vibration systems with super-quadratic potential. We obtain at least two nonzero periodic solutions through the minimization method and Morse theory. Moreover, if the potential is even with respect to the spatial variables, by applying a minimax type theorem, we can obtain a stronger multiplicity result with the number of solutions linked to the Morse index at zero.