Stavroulakis, I. P. Oscillations of functional differential equations. (English) Zbl 0902.34062 Mem. Differ. Equ. Math. Phys. 12, 196-203 (1997). The author establishes some oscillation criteria (without proofs) for linear delay differential equations \[ x'(t)+ p(t)x(\tau (t)) =0, \qquad \tau(t) <t,\quad t\geq t_0 \tag{*} \] and its discrete analogue \[ x_{n+1}-x_n+p_nx_{n-k}=0, \qquad k\in \mathbb{Z}^+, \tag{**} \] respectively, under some conditions which contain the following: (i) \(\liminf_{t\to \infty} \int^t_{\tau(t)} p(s)ds \leq \frac 1e\) and \(\limsup_{t\to \infty} \int^t_{\tau(t)} p(s)ds <1\); (ii) \(\liminf_{n\to \infty} \sum^{n-1}_{i=n-k} p_i \leq (\frac k{k+1})^{k+1} \) and \(\limsup_{n\to \infty}\sum^n_{i=n-k} p_i < 1\), respectively. This work is related to L. H. Erbe and B. G. Zhang [Differ. Integral Equ. 1, No. 3, 305-314 (1988; Zbl 0723.34055); ibid. 2, No. 3, 300-309 (1989; Zbl 0723.39004)]. Reviewer: Rong Yuan (Beijing) MSC: 34K11 Oscillation theory of functional-differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34K25 Asymptotic theory of functional-differential equations Keywords:oscillations; FDE; difference equations Citations:Zbl 0723.39004; Zbl 0723.34055 PDFBibTeX XMLCite \textit{I. P. Stavroulakis}, Mem. Differ. Equ. Math. Phys. 12, 196--203 (1997; Zbl 0902.34062) Full Text: EuDML EMIS