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

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 t...

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Bibliographic Details
Published in:Advances in difference equations 2008-01, Vol.2008, p.1-19
Main Authors: Došlý, Ondřej, Fišnarová, Simona
Format: Article
Language:English
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Summary: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.
ISSN:1687-1839
1687-1847
DOI:10.1155/2008/438130