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On a Functional-Differential Equation of A. F. Beardon and Functional-Differential Equations of Briot–Bouquet Type

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Abstract

We look for solutions of the functional-differential equation \(f(\varphi (z))=a(z)f(z)f^\prime (z)\) for given series \(\varphi \) and \(a\). We show that all formal solutions \(f\) of this equation are local analytic. In order to do this we transform the equation to a special type of Briot–Bouquet differential equation.

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Authors and Affiliations

  1. Institute of Mathematics and Scientific Computing, Karl-Franzens-University Graz, Heinrichstraße 36, 8010 , Graz, Austria

    Ludwig Reich

  2. Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359 , Luxembourg, Grand Duchy of Luxembourg

    Jörg Tomaschek

Authors
  1. Ludwig Reich
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  2. Jörg Tomaschek
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Corresponding author

Correspondence to Jörg Tomaschek.

Additional information

Communicated by Alan F. Beardon.

J. Tomaschek is supported by the National Research Fund, Luxembourg (AFR 3979497), and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND).

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Reich, L., Tomaschek, J. On a Functional-Differential Equation of A. F. Beardon and Functional-Differential Equations of Briot–Bouquet Type. Comput. Methods Funct. Theory 13, 383–395 (2013). https://doi.org/10.1007/s40315-013-0025-z

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  • DOI: https://doi.org/10.1007/s40315-013-0025-z

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