On some constants for oscillation and stability of delay equations

Berezansky, Leonid; Braverman, Elena

doi:10.1090/S0002-9939-2011-10820-7

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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