Oscillation of solutions to nonlinear first-order delay differential equations

Abstract

In this article, we present sufficient conditions for the oscillation of all solutions to the delay differential equation

$$x^{\prime }\left(t\right)+\sum _{i=1}^n{f}_i\left(t,x\left({\tau }_i\left(t\right)\right)\right)=0,t\ge t_0.$$

In particular, we extend known results from linear to nonlinear equations, and improve the bounds of previous criteria.