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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
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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