Article citationsMore>>

Tang, C. and Wu, X. (2010) Some Critical Point Theorems and Their Applications to Periodic Solution for Second Order Hamiltonian Systems. Journal of Differential Equations, 248, 660-692.
https://doi.org/10.1016/j.jde.2009.11.007

has been cited by the following article:

• 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.