2004 Conference on Diff. Eqns. and Appl. in Math. Biology, Nanaimo,
BC, Canada.
Electronic Journal of Differential Equations,
Conference 12, 2005, pp. 21-17.
Title: Oscillation and asymptotic stability of a delay differential
equation with Richard's nonlinearity
Authors: Leonid Berezansky (Ben-Gurion Univ. of the Negev, Israel)
Lev Idels (Malaspina Univ., Nanaimo, BC, Canada)
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.