Abstract
In this article, we consider the second-order nonlinear neutral delay dynamic equation (Formula presented.) on a time scale (Formula presented.) and establish some new oscillation and nonoscillation criteria. Also from these we deduce the Leighton–Wintner, Hille–Kneser, Kamenev, and Philos types oscillation criteria. Our results are different and complement the existence oscillation results for neutral delay dynamic equations on time scales in (Agarwal et al. 2004, Oscillation criteria for second-order nonlinear neutral dynamic equations. Journal of Mathematical Analysis and Applications, 300, 203–217) and (S.H. Saker, 2006, Oscillation of second-order nonlinear neutral delay dynamic equations on time scales. Journal of Computational and Applied Mathematics, 187, 123–141). Our results can be applied on the time scales (Formula presented.), (Formula presented.), (Formula presented.), for h > 0, (Formula presented.) (Formula presented.) (Formula presented.), (Formula presented.), (Formula presented.), and when (Formula presented.) where {t n } is the set of harmonic numbers, etc. Some examples are considered to illustrate the main results.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | International Journal of Phytoremediation |
| Volume | 86 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2007 |
Keywords
- 2000 AMS Subject Classifications: 34K11
- 39A10
- 39A99 (34A99; 34C10; 39A11)
- Oscillation
- Second-order neutral nonlinear dynamic equation
- Time scales
Authors (Note for portal: view the doc link for the full list of authors)
- Authors
- Saker, SH;Agarwal, RP;O'Regan, D