Some notes on oscillation of two-dimensional system of difference equations

Zdeněk Opluštil

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Half-linear discrete oscillation theory.

Řehák, Pavel (2000)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Linearized Riccati technique and (non-)oscillation criteria for half-linear difference equations.

Došlý, Ondřej, Fišnarová, Simona (2008)

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Oscillatory nonautonomous Lucas sequences.

Ferreira, José M., Pinelas, Sandra (2010)

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Oscillation criteria for first-order forced nonlinear difference equations.

Agarwal, Ravi P., Grace, Said R., Smith, Tim (2006)

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Oscillatory properties of second order half-linear difference equations

Pavel Řehák (2001)

Czechoslovak Mathematical Journal

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We study oscillatory properties of the second order half-linear difference equation $Δ (r_{k} | Δ y_{k} |^{α - 2} Δ y_{k}) - p_{k} {| y_{k + 1} |}^{α - 2} y_{k + 1} = 0, α > 1 . (HL)$ It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation $Δ (r_{k} Δ y_{k}) - p_{k} y_{k + 1} = 0 .$ We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.

On the oscillation of certain third-order difference equations.

Agarwal, Ravi P., Grace, Said R., O'Regan, Donal (2005)

Advances in Difference Equations [electronic only]

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