×

Some oscillation criteria for first order delay dynamic equations. (English) Zbl 1080.39005

The author presents a generalization and extension of two results regarding the oscillation criteria for first-order delay dynamic equations of the form \[ y^\Delta(t)+ p(t) y(r(t))= 0, \] where \(t\in T\), \(T\) is time scale that is unbounded above, \(p\) is rd-continuous and positive, \(r: T\to T\) is the delay function (\(r(t)< t\) \(\forall t\in T\) and \(\lim_{t\to\infty}\,r(t)= \infty\)), and \(y^\Delta(t)\) is the delta derivative of \(y: T\to T\) at \(t\in T\). The results are illustrated by applying them to various kinds of time scales.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
PDFBibTeX XMLCite