On a nonlinear delay population model

The nonlinear delay differential equation x˙(t)=r(t)[g(t,xt)−h(x(t))],t≥0 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.