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arXiv · 2112.02528

Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

Sergey Gefter·Anna Goncharuk
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Abstract

Consider the linear differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution of this equation from $K[[x]]$. Also the fundamental solution from $\frac{1}{x}K[[\frac{1}{x}]]$ of the equation is obtained and it is shown that the convolution of the fundamental solution and a non-homogeneity is a unique solution of the equation.

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Sergey Gefter, Anna Goncharuk. 2021-12-05. Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation. https://arxiv.org/abs/2112.02528

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