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

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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References

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Author information

Correspondence to Jörg Tomaschek.

Additional information

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).

Communicated by Alan F. Beardon.

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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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Keywords

  • Functional-differential equations
  • Briot–Bouquet equations

Mathematics Subject Classification (2000)

  • 34K17
  • 34M25
  • 30D05