On the asymptotic behavior of solutions of a nonlinear difference-differential equation

Sufficient conditions are established on the asymptotic behavior of solutions of the nonlinear delay differential equationx′(t)+p(t)f(x(t−τ))=0,t≥0, where τ∈(0,∞),p∈C([0,∞),[0,∞)),f∈C(R,R) and xf(x)>0 if x≠0. Some applications are given.