## International Journal of Differential Equations

### Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales

#### Abstract

This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation ${(r(t){({x}^{\mathrm{\Delta }}(t))}^{\gamma })}^{\mathrm{\Delta }}+p(t){x}^{\gamma }(g(t))=0$ on an arbitrary time scale $\mathrm{𝕋}$ with sup $\mathrm{𝕋}=\infty$, where $g(t)\ge t$ and ${\int }_{{t}_{o}}^{\infty }(\mathrm{\Delta }s/({}_{r}1/{\gamma }_{(s)}))<\infty$. 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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 840569, 16 pages.

Dates
Revised: 7 July 2011
Accepted: 26 July 2011
First available in Project Euclid: 25 January 2017

https://projecteuclid.org/euclid.ijde/1485313235

Digital Object Identifier
doi:10.1155/2011/840569

Mathematical Reviews number (MathSciNet)
MR2832513

Zentralblatt MATH identifier
1239.34111

#### Citation

Tang, Shuhong; Li, Tongxing; Thandapani, Ethiraju. Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales. Int. J. Differ. Equ. 2011 (2011), Article ID 840569, 16 pages. doi:10.1155/2011/840569. https://projecteuclid.org/euclid.ijde/1485313235

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