Advances in Difference Equations
Volume 2008 (2008), Article ID 438130, 18 pages
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

Academic Editor: John R. Graef

Copyright © 2008 Ondřej Došlý and Simona Fišnarová. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the half-linear second-order difference equation Δ(rkΦ(Δxk))+ckΦ(xk+1)=0, Φ(x):=|x|p2x, 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.