Delay differential logistic equation with linear harvesting

In this paper, we consider a logistic delay equation with a linear delay harvesting term of the following form:$\dot{N}(t)=r(t)N(t)\left.a-b_{0}N(t)-\sum _{k=1}^m{b}_{k}N(h_k(t))\right]-\sum _{l=1}^n{c}_l(t)N(g_l(t)),t?0\text{,}$$N(t)=\phi (t),t<0,N(0)=N_0$in both cases when $b_0=0$ and $b_0\ne 0$. We present some results on the boundedness and positiveness of the solutions of this equation without the condition that $N_0$ is upper bounded by some constant which is necessary to the corresponding results in L. Berezansky, E. Braverman, L. Idels, Delay differential logistic equation with harvesting, Math. Comput. Modelling 40 (2004) 1509–1525], and our results extend these known results.