Oscillation of delay differential equations via the hyper4 convergence

A sharp condition is provided to guarantee that the (nontrivial) solutions of a DDE of the form $\dot{x}(t)+F(t,x)=0$ $t\geq 0,$ (where $F(t,\cdot)$ is an odd-like causal operator) either oscillate, or converge monotonically to zero. The method used is based on the convergence of the sequence of hyper4-iterations to the Lambert's function.