New nonoscillation criteria for delay differential equations.
The authors consider first-order delay differential equations of the form \[ x'(t)+p(t)x(\tau(t))=0,\quad t\geq t_0, \] where \(p, \tau\in C([t_0, \infty), [0, \infty)), \tau(t)\) is nondecreasing, \(\tau(t)<t\) for \(t\geq t_0\) and \(\lim_{t\rightarrow\infty}\tau(t)=\infty\). When the well-known nonoscillation condition \(\int_{\tau(t)}^t p(s)\,ds\leq 1/e\) is not satisfied, some new nonoscillation conditions are obtained for the equations and they improve a number of existing results.
scientific article; zbMATH DE number 2055358
scientific article