Oscillation criteria for delay equations
Mark Kon, Yiannis G. Sficas, Ioannis P. Stavroulakis · Proceedings of the American Mathematical Society · 2000
This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form \begin{eqnarray} x’ (t)+p(t)x({\tau }(t))=0, \quad t\geq t_{0}, \end{eqnarray} where $p, {\tau } \in C([t_{0}, \infty ), \mathbb {R}^+), \mathbb {R}^+=[0, \infty ), \tau (t)$ is non-decreasing, $\tau (t) 2k+\frac {2}{{\lambda }_{1}}-1 \] holds, where ${\lambda _1}$ is the smaller root of the equation $\lambda =e^{k \lambda }$.