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A note on periodic solutions of Riccati equations

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    M. R. Mokhtarzadeh, M. R. Pournaki & A. Razani

  2. Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran

    M. R. Pournaki

  3. Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin, Iran

    A. Razani

Authors
  1. M. R. Mokhtarzadeh
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  2. M. R. Pournaki
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  3. A. Razani
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Corresponding author

Correspondence to M. R. Pournaki.

Additional information

The research of M.R. Pournaki and A. Razani was in part supported by a grant from IPM (Nos. 86200111 and 86340022).

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Mokhtarzadeh, M.R., Pournaki, M.R. & Razani, A. A note on periodic solutions of Riccati equations. Nonlinear Dyn 62, 119–125 (2010). https://doi.org/10.1007/s11071-010-9703-9

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  • DOI: https://doi.org/10.1007/s11071-010-9703-9

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