Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

Anatoly N. Kochubei

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Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

Anatoly N. Kochubei

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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 $u\circ u\circ ... \circ u$ of the 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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BibTeX RIS

Anatoly N. Kochubei. 2004-05-28. Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field. https://arxiv.org/abs/math/0405542

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