nonlinear delay differential equation
is considered. Sufficient conditions are established for the uniform permanence
of the positive solutions of the equation. In several particular cases, explicit
formulas are given for the upper and lower limit of the solutions. In some
special cases, we give conditions which imply that all solutions have the same
asymptotic behavior, in particular, when they converge to a periodic or constant
steady-state. Our equation contains the logistic equation in mathematical ecology which is a prototype
in modeling the dynamics of single species population systems