Vol. 66, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Oscillation criteria for second order self adjoint differential systems

Garret J. Etgen and James Pawlowski

Vol. 66 (1976), No. 1, 99–110
Abstract

Let be a Hilbert space and let = (,) be the Banach algebra of bounded linear operators from to with the usual operator norm. Let 𝒮 be the subspace of consisting of the self adjoint operators, and consider the second order differential system

Y′′ + P(x)Y = 0
(1)

on R+ = [0,), where P : R+ →𝒮 is continuous. Let 𝒢 be the set of positive linear functionals on . The elements of 𝒢 are used to derive oscillation criteria for this differential system. These criteria include a large number of well-known oscillation criteria for corresponding matrix differential systems and scalar equations. Extensions of the results to nonlinear differential systems and differential inequalities are also discussed.

Mathematical Subject Classification 2000
Primary: 34G05, 34G05
Secondary: 34C10
Milestones
Received: 9 March 1976
Published: 1 September 1976
Authors
Garret J. Etgen
James Pawlowski