## 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.## References

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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