Opuscula Math. 32, no. 2 (2012), 357-375
http://dx.doi.org/10.7494/OpMath.2012.32.2.357

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
• Revised: 2011-06-15.
• Accepted: 2011-06-15.