Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

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.