Nonlinear Dynamics

, Volume 62, Issue 1–2, pp 119–125 | Cite as

A note on periodic solutions of Riccati equations

Original Paper


In this note, we show that under certain assumptions the scalar Riccati differential equation x′=a(t)x+b(t)x 2+c(t) with periodic coefficients admits at least one periodic solution. Also, we give two illustrative examples in order to indicate the validity of the assumptions.


Scalar Riccati differential equation Periodic solution Banach space Compact operator Schauder’s fixed point theorem 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • M. R. Mokhtarzadeh
    • 1
  • M. R. Pournaki
    • 1
    • 2
  • A. Razani
    • 1
    • 3
  1. 1.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of Mathematical SciencesSharif University of TechnologyTehranIran
  3. 3.Department of Mathematics, Faculty of ScienceImam Khomeini International UniversityQazvinIran

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