Differential Equations

, Volume 49, Issue 1, pp 126–131 | Cite as

Weak periodic shift operator and generalized-periodic motions

  • A. P. Afanas’ev
  • S. M. Dzyuba
Short Communications


We introduce the notions of a weak periodic system and its generalized-periodic motions. Such systems include systems generated by ordinary differential equations, equations with retarded argument, Volterra type equations, etc. We present a criterion for the existence of generalized-periodic motions and establish their main properties.


Periodic Solution Periodic Motion Periodic System Shift Operator Nonautonomous System 
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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • A. P. Afanas’ev
    • 1
    • 2
    • 3
  • S. M. Dzyuba
    • 1
    • 2
    • 3
  1. 1.Institute of Systems AnalysisRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.Tambov State Technical UniversityTambovRussia

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