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Analytic Solutions of an Iterative Functional Differential Equation near Resonance

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  • Tongbo Liu
  • Hong Li

Abstract

We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function ð ‘¥ î…ž î…ž ( 𠑧 ) + ð ‘ ð ‘¥ î…ž ( 𠑧 ) = ð ‘¥ ( ð ‘Ž 𠑧 + ð ‘ ð ‘¥ ( 𠑧 ) ) in the complex field â„‚ . By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function 𠜆 2 ð ‘” î…ž î…ž ( 𠜆 𠑧 ) ð ‘” î…ž ( 𠑧 ) − 𠜆 ð ‘” î…ž ( 𠜆 𠑧 ) ð ‘” î…ž î…ž ( 𠑧 ) + ð ‘ ( ð ‘” î…ž ( 𠑧 ) ) 2 ( 𠜆 ð ‘” î…ž ( 𠜆 𠑧 ) − ð ‘Ž ð ‘” î…ž ( 𠑧 ) ) = ( ð ‘” î…ž ( 𠑧 ) ) 3 ( ð ‘” ( 𠜆 2 𠑧 ) − ð ‘Ž ð ‘” ( 𠜆 𠑧 ) ) , we get its local invertible analytic solutions.

Suggested Citation

  • Tongbo Liu & Hong Li, 2009. "Analytic Solutions of an Iterative Functional Differential Equation near Resonance," International Journal of Differential Equations, Hindawi, vol. 2009, pages 1-14, June.
    • Handle: RePEc:hin:jnijde:145213
    DOI: 10.1155/2009/145213
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    Cited by:

    1. Jiraphorn Somsuwan & Keaitsuda Maneeruk Nakprasit, 2015. "Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, October.

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