Vol. 17, No. 3, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
The behavior of solutions of the differential equation y′′′ + p(x)y + q(x)y = 0

Alan Cecil Lazer

Vol. 17 (1966), No. 3, 435–466

This paper is a study of the oscillation and other properties of solutions of the differential equation

y′′′ + p(x)y′ +q(x)y = 0.

Throughout, we shall assume that p(x) and q(x) are continuous and do not change sign on the infinite half-axis I : a x < +. A solution of (L) will be said to be oscillatory if it change sign for arbitrarily large values of x.

Our principal results will be concerned with the existence, uniqueness, (aside from constant multiples) and asymptotic behavior of nontrivial, nonoscillatory solutions, and criteria for the existence of oscillatory solutions in terms of the behavior of nonoscillatory solutions. Other results are concerned with separation properties and the question of when the amplitudes of oscillatory solutions are increasing or decreasing.

Mathematical Subject Classification
Primary: 34.42
Received: 2 June 1964
Published: 1 June 1966
Alan Cecil Lazer