Solving Linear Differential Equations

K. A. Nguyen, Marius van der Put

Type: Article

Publication Date: 2010-01-01

Citations: 10

DOI: https://doi.org/10.4310/pamq.2010.v6.n1.a5

Abstract

The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galois theory are the main tools.The results extend the classical work of G. Fano.

Locations

Pure and Applied Mathematics Quarterly - View - PDF
arXiv (Cornell University) - PDF

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+ PDF Chat	Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz	2020	Moulay A. Barkatou Thomas Cluzeau Lucia Di Vizio Jacques-Arthur Weil
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+ PDF Chat	A characterization of reduced forms of linear differential systems	2012	Ainhoa Aparicio-Monforte Élie Compoint Jacques-Arthur Weil
+	Linear differential equations with finite differential Galois group	2020	Marius van der Put Camilo Sanabria Jaap Top
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+ PDF Chat	Solving order 3 difference equations	2025	Heba Bou KaedBey Mark van Hoeij Man Cheung Tsui

Works Cited by This (5)

Action	Title	Year	Authors
+ PDF Chat	Algebraic relations among solutions of linear differential equations	1986	Michael F. Singer
+	Absolute reducibility of differential operators and Galois groups	2004	Élie Compoint J-A Weil
+	Ueber lineare homogene Differentialgleichungen mit algebraischen Relationen zwischen den Fundamentall�sungen	1900	Gino Fano
+	Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations	1985	Michael F. Singer
+	Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem	1988	Michael F. Singer