On the index and the order of quasi-regular implicit systems of differential equations

LISI D'ALFONSO; GABRIELA JERONIMO; GUSTAVO MASSACCESI; PABLO SOLERNÓ

LINEAR ALGEBRA AND ITS APPLICATIONS

Elsevier

Año: 2009 vol. 430 p. 2102 - 2122

0024-3795

This paper is mainly devoted to the study of the differentiationindex and the order for quasi-regular implicit ordinary differentialalgebraic equation (DAE) systems. We give an algebraic definition ofthe differentiation index and prove a Jacobi-type upper bound forthe sum of the order and the differentiation index. Our techniquesalso enable us to obtain an alternative proof of a combinatorialbound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for theHilbert-Kolchin regularity and an effective ideal membership testfor quasi-regular implicit systems. Finally, we prove a theorem ofexistence and uniqueness of solutions for implicit differentialsystems.