Notes on Multiple Periodic Solutions for Second Order Hamiltonian Systems

• Yiwei Ye ^[1] ; Shan Liu ^[1]
  1. [1] Chongqing Normal University

     Chongqing Normal University

     China

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

  • In this paper, we study the multiplicity of periodic solutions for the second order Hamiltonian systems u¨ + ∇F(t, u) = 0 with the boundary condition u(0) − u(T ) = u˙(0) − ˙u(T ) = 0, where the potential F is either subquadratic k(t)-concave or subquadratic μ(t)-convex. Based on the reduction method and a three-critical-point theorem due to Brezis and Nirenberg, we obtain the multiplicity results, which complement and sharply improve some related results in the literature.

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