Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-15T07:28:37.008Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on an Oscillation Criterion for anEquation with a Functional Argument

Published online by Cambridge University Press:  20 November 2018

Paul Waltman
Paul Waltman*
Affiliation:
University of Iowa
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It might be thought that, as far as the oscillation of solutions is concerned, the behaviour of

and

would be the same as long as t - α(t) → ∞ as t→∞. To motivate the theorem presented in this note, we show first that this is not the case. Consider the above equation with α(t) = 3t/4, a(t) = l/2t2 i.e.

This equation has the non-oscillatory solution y(t) = t1/2 although all solutions of

are oscillatory [1, p. 121].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 593 - 595
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bellman, R., Stability Theory of Differential Equations. (McGraw Hill, 1953).Google Scholar