Advances in Difference Equations (Jan 2008)

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

  • Fišnarová Simona,
  • Došlý Ondřej

Journal volume & issue
Vol. 2008, no. 1
p. 438130

Abstract

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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.