COMPONENT-WISE CONDITIONS FOR THE ASYMPTOTIC EQUIVALENCE FOR NONLINEAR DIFFERENTIAL SYSTEMS WITH MAXIMA

TitleCOMPONENT-WISE CONDITIONS FOR THE ASYMPTOTIC EQUIVALENCE FOR NONLINEAR DIFFERENTIAL SYSTEMS WITH MAXIMA
Publication TypeJournal Article
Year of Publication2011
AuthorsGONZÁLEZ PATRICIO, PINTO MANUEL
JournalDynamic Systems and Applications
Volume20
Start Page439
Pagination15
Date Published2011
ISSN1056-2176
AMS Subject Classification34A20, 34A30, 34A36, 34C41, 34D05
Abstract

We obtain new sufficient component-wise conditions for the asymptotic equivalence between bounded solutions of linear and nonlinear systems of differential equations with maxima. A Lipschitz component-wise and a spectral condition allow us to obtain vectorial asymptotic formulae. Under a spectral dichotomy condition the equivalences take the form of a homeomorphism which is also extended to unbounded solutions. We also obtain a vectorial Levinson’s theorem with maximum about asymptotic integration.

PDFhttps://acadsol.eu/dsa/articles/20/29-DSA-30-04.pdf
Refereed DesignationRefereed