On the oscillation of delay differential equations with real coefficients (Q1587817)

The author investigates oscillatory properties of the delay differential equation \[ x'(t)+\sum_{i=1}^{l}p_i x(t-\tau_i)+\sum_{j=1}^{r}q_j x(t-\sigma_j)=0, \tag{*} \] where \(p_i,\tau_i,q_j\) and \(\sigma_j\in \mathbb{R}^+\), \(i=1,2,\dots,l\), \(j=1,2,\dots,r\) with \(l+r=n\), \(\tau_i\geq 0\), \(\sigma_j\geq 0\). There is given a set of necessary conditions and another set of sufficient conditions for the oscillation of all solutions to (*). The obtained results extend results of \textit{O.~Arino} and \textit{I.~Györi} [J. Differ. Equations 81, No. 1, 98-105 (1989; Zbl 0691.34054)] and of \textit{I.~Györi} and \textit{G.~Ladas} [Oscillation theory of delay differential equations: with applications. Oxford: Clarendon Press (1991; Zbl 0780.34048)].