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Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

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Abstract

In earlier papers, the author studied some classes of equations with Carlitz derivatives for \(\mathbb{F}_q\)-linear functions, which are the natural function-field counterparts of linear ordinary differential equations. Here we consider equations containing self-compositions u ∘ u ... ∘ u of an unknown function. As an algebraic background, imbeddings of the composition ring of \(\mathbb{F}_q\)-linear holomorphic functions into skew fields are considered.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    A. N. Kochubei

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  1. A. N. Kochubei
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 669–678, May, 2005.

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Kochubei, A.N. Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field. Ukr Math J 57, 794–805 (2005). https://doi.org/10.1007/s11253-005-0229-0

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  • DOI: https://doi.org/10.1007/s11253-005-0229-0

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