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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On some constants for oscillation and stability of delay equations


Authors: Leonid Berezansky and Elena Braverman
Journal: Proc. Amer. Math. Soc. 139 (2011), 4017-4026
MSC (2010): Primary 34K11, 34K20
Published electronically: March 28, 2011
MathSciNet review: 2823047
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Abstract: We discuss the famous constants of $ 1/e$, 1, $ 3/2$ in necessary and/or sufficient oscillation and stability conditions for delay differential equations with one or more delays:

$\displaystyle x^{\prime }(t)= - \sum_{k=1}^ma_k(t) x(t-h_k(t)), $

including equations with oscillatory coefficients. Some counterexamples (which refer to necessary oscillation and stability conditions) are presented and open problems are stated.


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Additional Information

Leonid Berezansky
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Elena Braverman
Affiliation: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada
Email: maelena@math.ucalgary.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10820-7
PII: S 0002-9939(2011)10820-7
Keywords: Delay equations, stability, oscillation, non-oscillation, oscillatory coefficients
Received by editor(s): December 17, 2009
Received by editor(s) in revised form: September 30, 2010
Published electronically: March 28, 2011
Additional Notes: The first author was partially supported by the Israeli Ministry of Absorption.
The second author was partially supported by an NSERC Research Grant and is the corresponding author.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.