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Zbl 0719.34118
On the oscillation and asymptotic behavior of $\dot N(t)=N(t)[a+bN(t- \tau)-cN\sp 2(t-\tau)]$.
(English)
[J] Q. Appl. Math. 48, No.3, 433-440 (1990). ISSN 0033-569X; ISSN 1552-4485/e

The authors study the equation $(1)\quad N'(t)=N(t)(a+bN(t-\tau)-cN\sp 2(t-\tau)),$ where $a,c\in (0,\infty)$, $c\in {\bbfR}$, $\tau\in [0,\infty)$. They give sufficient conditions for all positive solutions of (1) to oscillate about its positive equilibrium $N\sp*$ and also derive sufficient conditions for all positive solutions of (1) to converge to $N\sp*$ as $t\to \infty$.
[P.Marušiak (Žilina)]
MSC 2000:
*34K99 Functional-differential equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: differential equation with retarded argument; oscillatory and nonoscillatory solution

Cited in: Zbl 0898.92023

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