Existence of Periodic Solutions for the Forced Pendulum Equations of Variable Length

• Hujun Yang ^[1] ; Xiaoling Han ^[1]
  1. [1] Northwest Normal University

     Northwest Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This article investigates the forced pendulum equations of variable length x + kx + a(t)sin x = e(t), where a(t), e(t) are continuous T -periodic functions, k ∈ R is a constant. Under suitable assumptions on the a(t), e(t) and T , we prove the existence of T -periodic solutions to the forced pendulum equations using Mawhin’s continuation theorem.

    Finally, some specific examples and numerical simulations are given to illustrate the applicability of the conclusions of this paper.