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Transcendental Meromorphic Solutions of P 34 and Small Targets

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Analytic, Algebraic and Geometric Aspects of Differential Equations

Part of the book series: Trends in Mathematics ((TM))

Abstract

The equation P 34 is closely related to the well-known second Painlevé equation P 2 and some properties of its meromorphic solutions are similar to those of the solutions of P 4. We discuss various value distribution properties of solutions of P 34, including growth, the second main theorem and behaviour towards small target functions.

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Acknowledgements

Galina Filipuk acknowledges the support of the National Science grant 2011/03/B/ST1/00330.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Szczecin, ul. Wielkopolska 15, 70-451, Szczecin, Poland

    Ewa Ciechanowicz

  2. Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Galina Filipuk

  3. Institute of Mathematics of the Polish Academy of Sciences, Sniadeckich str. 8, 00-956, Warsaw, Poland

    Galina Filipuk

Authors
  1. Ewa Ciechanowicz
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  2. Galina Filipuk
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Corresponding author

Correspondence to Galina Filipuk .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Kumamoto University, Kumamoto, Japan

    Yoshishige Haraoka

  3. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

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Ciechanowicz, E., Filipuk, G. (2017). Transcendental Meromorphic Solutions of P 34 and Small Targets. In: Filipuk, G., Haraoka, Y., Michalik, S. (eds) Analytic, Algebraic and Geometric Aspects of Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52842-7_6

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