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

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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