On Noetherian index of differential/algebraic systems. I
type: Item
instance of: scholarly article
title: On Noetherian index of differential/algebraic systems. I
zbMATH Open document ID: 0805.34001
DOI: 10.1007/BF00971234
published in: Siberian Mathematical Journal
publication date: 1994-10-05T00:00:00Z
review text: Under consideration is the problem \(\Lambda x : = A(t) \dot x + B(t)x = f\), \(t \in T = [\alpha, \beta]\), \(x(\alpha) = a\), where \(A(t)\) and \(B(t)\) and \((n \times n)\)-matrics whose smoothness will be specified in formulations, \(f \equiv f(t)\) and \(x \equiv x(t)\) are known and unknown \(n\)-dimensional vector-functions, and the dot denotes differentiation with respect to \(t\). We suppose that \(\text{det} A(t) = 0\) \(\forall t \in T\). In the present article we study properties of the operators \(\Lambda : E \to F\) and \(\Lambda_ a : E \to F \times \mathbb{R}^ n\), where \(\Lambda_ ax = \{\Lambda x; x(\alpha)\}\), \(E\) and \(F\) are topological vector or Banach spaces, and in the first case \(E=F=C^ \infty(T)\), and in the second case \(E=C^ 1(T)\) and \(F=\Lambda C^ 1(T)\).
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 641323
zbMATH Keywords: noetherian index
zbMATH Keywords: differential/algebraic systems
author: V. F. Chistyakov
MaRDI profile type: Publication
cites work: Differential/Algebraic Equations are not ODE’<scp>s</scp>
cites work: Canonical Forms and Solvable Singular Systems of Differential Equations
cites work: Q3900330
cites work: Q3787380
cites work: Q3993124
full work available at URL: https://doi.org/10.1007/bf00971234
OpenAlex ID: W1966086699
description: scientific article; zbMATH DE number 641323