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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On some constants for oscillation and stability of delay equations
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by Leonid Berezansky and Elena Braverman PDF
Proc. Amer. Math. Soc. 139 (2011), 4017-4026 Request permission

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: \[ x^{\prime }(t)= - \sum _{k=1}^ma_k(t) x(t-h_k(t)), \] 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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 4017-4026
  • MSC (2010): Primary 34K11, 34K20
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10820-7
  • MathSciNet review: 2823047