New Periodic Solutions of Singular Hamiltonian Systems with Fixed Energies

2011/11/26 by Fengying Li, Li, Fengying, Qingqing Hua +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1111.6169

openalex publication_date 2011/11/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential V∈ C²(Rⁿ\backslash O,R) and V∈ C¹(R²\backslash O,R) which may have an unbounded potential well, and prove the existence of non-trivial periodic solutions with a prescribed energy. Our results can be regarded as some complements of the well-known Theorems of Benci-Gluck-Ziller-Hayashi and Ambrosetti-Coti Zelati and so on.

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