Abstract
This paper is concerned with the oscillatory behavior of the second‐order half‐linear advanced dynamic equation on an arbitrary time scale 𝕋 with sup 𝕋 = ∞, where g(t) ≥ t and . Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second‐order half‐linear advanced differential equation and the second‐order half‐linear advanced difference equation. Three examples are included to illustrate the main results.
Highlights
The study of dynamic equations on time scales, which has recently received a lot of attention, was introduced by Hilger 1 in order to unify continuous and discrete analysis
There has been much research activity concerning the oscillation of solutions of various dynamic equations on time scales, we refer the reader to the papers 5–18 and the references therein
Since we are interested in oscillatory behavior, we assume throughout this paper that the given time scale T is unbounded above
Summary
The study of dynamic equations on time scales, which has recently received a lot of attention, was introduced by Hilger 1 in order to unify continuous and discrete analysis. Dynamic equations on a time scale have an enormous potential for applications such as in population dynamics. There has been much research activity concerning the oscillation of solutions of various dynamic equations on time scales, we refer the reader to the papers 5–18 and the references therein. Since we are interested in oscillatory behavior, we assume throughout this paper that the given time scale T is unbounded above. The authors obtained some sufficient conditions which guarantee that every solution x of 1.8 oscillates or limt → ∞x t 0 under the case when. We will establish some new oscillation criteria for 1.1 under the case when 1.10 holds. All functional inequalities considered in this note are assumed to hold eventually, that is, they are satisfied for all t large enough
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
