Opuscula Math. 32, no. 2 (2012), 357-375

Opuscula Mathematica

Planar nonautonomous polynomial equations IV. Nonholomorphic case

Paweł Wilczyński

Abstract. We give a few sufficient conditions for the existence of periodic solutions of the equation \(\dot{z}=\sum_{j=0}^n a_j(t)z^j-\sum_{k=1}^r c_k(t)\overline{z}^k\) where \(n \gt r\) and \(a_j\)'s, \(c_k\)'s are complex valued. We prove the existence of one up to two periodic solutions.

Keywords: periodic orbits, polynomial equations.

Mathematics Subject Classification: 34C25, 34C37.

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  • Paweł Wilczyński
  • Jagiellonian University, Institute of Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
  • Received: 2011-04-06.
  • Revised: 2011-06-15.
  • Accepted: 2011-06-15.
Opuscula Mathematica - cover

Cite this article as:
Paweł Wilczyński, Planar nonautonomous polynomial equations IV. Nonholomorphic case, Opuscula Math. 32, no. 2 (2012), 357-375, http://dx.doi.org/10.7494/OpMath.2012.32.2.357

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