Study and solution of degenerate systems of ordinary differential equations by means of a change of variables
type: Item
instance of: scholarly article
title: Study and solution of degenerate systems of ordinary differential equations by means of a change of variables
zbMATH Open document ID: 0856.34001
DOI: 10.1007/BF02106848
published in: Siberian Mathematical Journal
publication date: 1997-02-25T00:00:00Z
review text: For the system \(A(t) x'(t)+ B(t) x(t)= f(t)\), \(t\in T= [\alpha, \beta]\), with \(A(t)\) an \(n\times n\)-matrix degenerate for every \(t\in T\) (\(f(t)\) and \(x(t)\) are the given and sought \(n\)-dimensional vectors and \(B(t)\) is not full rank in general) the Cauchy problem \(x(\alpha)= a\) is studied. Only such degenerate systems whose solutions are independent of arbitrary vector-functions are considered (i.e. they have Cauchy-type solutions). Necessary and sufficient conditions for existence of the right resolving operator and its decomposition into a composition of first-order linear differential operators is established as well as some equivalence between the right and the left resolving operators. An algorithm for finding a resolving change of variables is proposed.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 917166
zbMATH Keywords: Cauchy problem
zbMATH Keywords: degenerate systems
zbMATH Keywords: right resolving operator
author: Alla Arkad'evna Shcheglova
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 917166