Vol. 15, No. 1, 1965

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
The asymptotic nature of the solutions of certain linear systems of differential equations

Allen Devinatz

Vol. 15 (1965), No. 1, 75–83
Abstract

Suppose y(t) = [A + V (t) + R(t)]y(t) is a system of differential equations defined on [0,), where A is a constant matrix, V (t) 0 as t and the norms of the matrices V (t) and R(t) are summable. If the roots of the characteristic polynomial of A are simple, then under suitable conditions on the real parts of the roots of the characteristic polynomials of A + V (t) a theorem of N. Levinson gives an asymptotic estimate of the behavior of the solutions of the differential system as t . In this paper Levinson’s theorem is improved by removing the condition that the characteristic roots of A are simple. Under suitable conditions on V (t) and R(t) and the characteristic roots of A + V (t), which reduce to Levinson’s conditions when the characteristic roots of A are simple, asymptotic estimates are obtained for the solutions of the given system.

Mathematical Subject Classification
Primary: 34.50
Milestones
Received: 3 February 1964
Published: 1 March 1965
Authors
Allen Devinatz