Existence of Response Solutions to Quasi-Periodically Forced Oscillator Equation

• Xingkui Shu ^[1]
  1. [1] Neijiang Normal University

     Neijiang Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 4, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper focuses on two oscillator equations with quasi-periodic forcing, and obtains their response solutions through the contraction mapping principle. For undamped systems, when the average of the forcing is non-zero, we obtain analytical solutions and highly differentiable solutions respectively according to the forcing being in different spaces.When the average of the forcing is zero, we need to impose a weak Diophantine condition on the frequency, but the solution obtained in the analytical space does not lose regularity. However, in the highly differentiable context, our solution loses a bit of regularity. For damped systems, we do not need the system to be strongly dissipative, nor do we impose arithmetic conditions on the frequency. We directly obtain the response solution without losing regularity.

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