2004 Conference on Diff. Eqns. and Appl. in Math. Biology, Nanaimo, BC, Canada.
Electron. J. Diff. Eqns., Conference 12, 2005, pp. 21-27.

Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity

Leonid Berezansky, Lev Idels

Abstract:
We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation
$$
 \frac{dN}{dt} = r(t)N(t)\Big[a-\Big(\sum_{k=1}^m b_k N(g_k(t))
 \Big)^{\gamma}\Big], $$
where $ g_k(t)\leq t$.

Published April 20, 2005.
Math Subject Classifications: 34K11, 34K20, 34K60.
Key Words: Delay differential equations; Richard's nonlinearity; oscillation; stability.

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Leonid Berezansky
Department of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
email: brznsky@cs.bgu.ac.il Phone 972-7-6461602 Fax 972-7-6281340
Lev Idels
Mathematics Department
Malaspina University-College
900 Fifth Street Nanaimo, BC V9R 5S5, Canada
email: lidels@shaw.ca Phone 250-753-3245 ext. 2429 Fax 250-740-6482

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