On oscillation of a food-limited population model with time delay. (English) Zbl 1026.34075

Berezansky, Leonid; Braverman, Elena

Abstr. Appl. Anal. 2003, No. 1, 55-66 (2003).

Explicit oscillation and nonoscillation conditions for the scalar nonlinear delay differential equation \[ N'(t)=r(t)N(t)\frac{K-N(h(t))}{K+s(t)N(g(t))} \] are established, where \(r(t)\geq 0\), \(s(t)\geq 0\) are Lebesgue measurable locally essentially bounded functions, \(h,g:[0,+\infty)\to \mathbb{R}\) are Lebesgue measurable functions, \(h(t)\leq t\), \(g(t)\leq t\),
\(\lim_{t\to +\infty}h(t)=+\infty\), \(\lim_{t\to +\infty}g(t)=+\infty\), and \(K>0\). Some generalization of the above-mentioned equation is considered, too.

Reviewer: Robert Hakl (Brno)

MSC:

34K11	Oscillation theory of functional-differential equations
92D25	Population dynamics (general)

Keywords:

oscillation criteria; nonoscillation criteria