Advances in Difference Equations
Volume 2008 (2008), Article ID 438130, 18 pages
doi:10.1155/2008/438130
Linearized Riccati technique and (non-)oscillation criteria for half-linear difference equations
Ondřej Došlý1
and Simona Fišnarová2
1Department of Mathematics and Statistics, Masaryk University, Janá {c}kovo nám. 2a, Brno 66295, Czech Republic
2Department of Mathematics, Mendel University of Agriculture and Forestry in Brno, Zem {e}d {e}lská 1, Brno 61300, Czech Republic
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.