Global attractivity in a nonlinear delay differential equation with applications

We establish a sufficient condition for the global attractivity of solutions of the following nonlinear delay differential equation equation(0.1)x′(t)=p(t)[f(x(t−τ))−g(x(t))],t≥0, where τ∈(0,∞),p∈C[[0,∞),(0,∞)]andf,g∈C[(a,∞),(0,∞)]wherea≥−∞. Applications to some differential equation models derived from mathematical biology are also given.