Exact Multiplicity and Stability of Periodic Solutions for Duffing Equation with Bifurcation Method

• Liang, Shuqing ^[1]
  1. [1] Jilin University

     Jilin University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 477-493
• Idioma: inglés
• DOI: 10.1007/s12346-018-0296-x
• Enlaces
  • Texto completo
• Resumen

  • Under some Lp-norms(p∈[1,∞]) assumptions for the derivative of the restoring force, the exact multiplicity and the stability of 2π-periodic solutions for Duffing equation are considered. The nontrivial 2π-periodic solutions of it are positive or negative, and the bifurcation curve of it is a unique reversed S-shaped curve. The class of the restoring force is extended, comparing with the class of L∞-norm condition. The proof is based on the global bifurcation theorem, topological degree and the estimates for periodic eigenvalues of Hill’s equation by Lp-norms(p∈[1,∞]).

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