Oscillation of first-order nonlinear differential equations with deviating arguments

This paper is devoted to the study of the oscillatory behavior of solutions of the first-order nonlinear functional differential equations

First, without assuming that the deviating arguments ${g_i}(t),1 \leqslant i \leqslant N$, are retarded or advanced, sufficient conditions are established for all solutions of (A) and (B) to be oscillatory.

Secondly, a characterization of oscillation of all solutions is obtained for equation (A) with $F \equiv 0$ and ${g_i}(t) > t,1 \leqslant i \leqslant N$, as well as for equation (B) with $F \equiv 0$ and ${g_i}(t) < t,1 \leqslant i \leqslant N$.