2017
Том 69
№ 9

All Issues

Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

Kochubei A. N.

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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 $u \circ u ... \circ u$ 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.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 5, pp 794-805.

Citation Example: Kochubei A. N. Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field // Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 669–678.

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