Advances in Difference Equations 
Volume 2008 (2008), Article ID 438130, 18 pages
doi:10.1155/2008/438130
Research Article

Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations

Ondřej Došlý1 and Simona Fišnarová2

 1Department of Mathematics and Statistics, Masaryk University, Janáčkovo nám. 2a, Brno 66295, Czech Republic
2Department of Mathematics, Mendel University of Agriculture and Forestry in Brno, Zemědělská 1, Brno 61300, Czech Republic
Received 23 August 2007; Accepted 26 November 2007

Recommended by John R. Graef

Abstract

We consider the half-linear second-order difference equation Δ(rkΦ(Δxk))+ckΦ(xk+1)=0, Φ(x):=|x|p−2x, p>1, where r, c are real-valued sequences. We associate with the above-mentioned equation a linear second-order difference equation and we show that oscillatory properties of the above-mentioned one can be investigated using properties of this associated linear equation. The main tool we use is a linearization technique applied to a certain Riccati-type difference equation corresponding to the above-mentioned one.