Delay Differential Logistic Equation With Linear Harvesting

In the recent several dozens years, the ecology question arouses people's interest day by day, like the population growth, exterminate, the disease dissemination and so on. In order to solve these actual problems, people have given many mathematical model to research. At present each domain has emerged a large quantities of scientific research achievement in biological mathematics, which impelled the ecology development.Because most populations are effected by the external environment, we should pay more attention to the mathematical models with harvest controls and delays. In this paper, we cosider a logistic delay equation with a linear delay harvesting term of the following form:with initial conditionN(t)=φ(t), t＜0, N(0)=N₀.When b₀=0 and b₀≠0, we can obtain two kinds of models. L.Berezansky has studied the existence and the boundedness of positive solution of above equation with the initial value No less than some constan. We present some results on the boundedness and positiveness of the solutions of this equation without the condition that No is upper bounded by some constant, consequently our results include the corresponding results in [3] and extend these known results.