On oscillation of a food-limited population model with time delay

Abstract

For a scalar nonlinear delay differential equation$\dot{N}\left(t\right)=r\left(t\right)N\left(t\right)\left(K-N\left(h\left(t\right)\right)\right)/\left(K+s\left(t\right)N\left(g\left(t\right)\right)\right)$, $r\left(t\right)\ge 0$, $k>0$, $h\left(t\right)\le \mathrm{t}$, $g\left(t\right)\le \mathrm{t}$ and some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. Coefficient $r\left(t\right)$ and delays are not assumed to be continuous.