Quasi-Periodic Solutions of Derivative Beam Equation on Flat Tori

• Yingte Sun ^[1]
  1. [1] Yangzhou University

     Yangzhou University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we consider a class of nonlinear beam equations on flat tori Td L, utt + 2u = (−)α f (ωt, x, (−)βu), 0 < α + β ≤ 1 and prove that the equation admits many quasi-periodic solutions with the non-resonant frequencies ω. The main proof is based on an abstract Nash-Moser type implicit function theorem developed in Berti and Bolle (Nonlinearity 25(9):2579–2613, 2012;

    J Eur Math Soc 15(1):229–286, 2013).