Open Access

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

Advances in Difference Equations20072008:438130

https://doi.org/10.1155/2008/438130

Received: 2 January 2007

Accepted: 23 August 2007

Published: 26 November 2007

Abstract

We consider the half-linear second-order difference equation , , , where , 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.

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Authors’ Affiliations

(1)
Department of Mathematics and Statistics, Masaryk University
(2)
Department of Mathematics, Mendel University of Agriculture and Forestry in Brno

Copyright

© O. Došlý and S. Fišnarová. 2008

This article is published under license to BioMed Central Ltd. 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.