## Oscillation criteria for functional differential equations

### Summary

Summary: Consider the first-order linear delay differential equation $$x'(t)+p(t)x(\tau (t))=0,\quad t\geq t_{0},$$ and the second-order linear delay equation $$x''(t)+p(t)x(\tau (t))=0,\quad t\geq t_{0},$$ where $$0<\liminf_{t\to \infty }\int_{\tau (t)}^{t}p(s)ds\leq \frac{1}{e} \quad \hbox{and}\quad \limsup_{t\to \infty }\int_{\tau (t)}^{t}p(s)ds<1,$$ and for the second-order equation when $$\liminf_{t\to \infty }\int_{\tau (t)}^{t}\tau (s)p(s)ds \leq \frac{1}{e}\quad \hbox{and}\quad \limsup_{t\to \infty }\int_{\tau (t)}^{t}\tau (s)p(s)ds<1\,.$$

34K11, 34C10

### Keywords/Phrases

oscillation, delay differential equations