A note on the Darboux theory of integrability of non-autonomous polynomial differential systems
type: Item
instance of: scholarly article
title: A note on the Darboux theory of integrability of non-autonomous polynomial differential systems
zbMATH Open document ID: 1263.34004
DOI: 10.1088/0951-7715/25/9/2615
author: Chara Pantazi
author: David Blázquez-Sanz
published in: Nonlinearity
publication date: 2012-10-10T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/150477
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 6092432
zbMATH Keywords: Darboux integrability
zbMATH Keywords: non-autonomous polynomial differential systems
MaRDI profile type: Publication
OpenAlex ID: W2081864444
review text: The authors give sufficient and necessary conditions for the existence of a Darboux first integral or a Darboux Jacobi multiplier for a polynomial vector field with some known algebraic invariant hypersurfaces. For the autonomous case, the classical result of Darboux is obtained as a corollary. For the non-autonomous case, the characterization improves a known criterium given by \textit{J. Llibre} and \textit{Ch. Pantazi} [J. Math. Phys. 50, No. 10, Paper No. 102705 (2009; Zbl 1283.34027)]. A possible generalization of the results presented in this work is via the results presented in [\textit{I. A. García} and \textit{J. Giné}, Appl. Math. Lett. 16, No. 7, 1137--1141 (2003; Zbl 1057.34002)].
reviewed by: Jaume Giné
description: scientific article; zbMATH DE number 6092432