  We study bounded, unbounded and blow-up solutions of a delay logistic
equation without assuming the dominance of the instantaneous feedback. It is
shown that there can exist an exponential (thus unbounded) solution for the
nonlinear problem, and in this case the positive equilibrium is always
unstable. We obtain a necessary and sufficient condition for the existence of
blow-up solutions, and characterize a wide class of such solutions. There is a
parameter set such that the non-trivial equilibrium is locally stable but not
globally stable due to the co-existence with blow-up solutions.
