Delay differential logistic equations with harvesting

The logistic delay equation with a linear delay harvesting term N . ( t ) = r ( t ) N ( t ) [ a − ∑ k = 1 m b k N ( h k ( t ) ) ] − ∑ l = 1 n c l ( t ) N ( g l ( t ) ) , t ≥ 0 , N ( t ) = φ ( t ) , t < 0 , N ( 0 ) = N 0 , is considered. The existence and the bounds of positive solutions are studied. Sufficient conditions for the extinction of the solution are presented.