Multiple Periodic Solution for a Class of Damped Vibration System  

作　　者：Zihan Zhang Yuanhao Wang Guanggang Liu Zihan Zhang;Yuanhao Wang;Guanggang Liu(School of Mathematical Sciences, Liaocheng University, Liaocheng, China)

机构地区：[1]School of Mathematical Sciences, Liaocheng University, Liaocheng, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第12期4291-4300,共10页应用数学与应用物理(英文)

摘　　要：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.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.

关 键 词：Damped Vibration Problems Morse Theory Critical Group Morse Index Minimization Method 

分 类 号：O17[理学—数学]