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Liu, G. and Shi, S. (2020) Existence and Multiplicity of Periodic Solutions for Damped Vibration Problems with Nonlinearity of Linear Growth. Applied Mathematics Letters, 107, Article ID: 106502.
https://doi.org/10.1016/j.aml.2020.106502

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.