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

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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Correspondence to Ondřej Došlý.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Došlý, O., Fišnarová, S. Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations. Adv Differ Equ 2008, 438130 (2007). https://doi.org/10.1155/2008/438130

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation