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Periodic, quasi-periodic and unbounded solutions of radially symmetric systems with repulsive singularities at resonance

  • Qihuai Liu
  • Pedro J. TorresEmail author
  • Dingbian Qian
Article

Abstract

In this paper, we are concerned with periodic solutions, quasi-periodic solutions and unbounded solutions for radially symmetric systems with singularities at resonance, which are 2π-periodic in time. The method is based on the qualitative analysis of Poincaré map with action-angle variables. The existence of infinitely many periodic and quasi-periodic solutions or unbounded motions depends on the oscillatory properties of a certain function.

Mathematics Subject Classification

34C25 34B15 

Keywords

Resonance Unbounded solution Quasi-periodic solution Periodic solution Isochronous system 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilinPeople’s Republic of China
  3. 3.Departamento de Matemáptica Aplicada, Facultad de CienciasUniversidad de GranadaGranadaSpain
  4. 4.School of Mathematical SciencesSoochow UniversitySuzhouPeople’s Republic of China

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