On the oscillation of certain third-order difference equations.

Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal

Displaying similar documents to “On the oscillation of certain third-order difference equations.”

Oscillation criteria for first-order forced nonlinear difference equations.

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

Advances in Difference Equations [electronic only]

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On oscillation of second order linear difference equations with deviated arguments.

Koplatadze, R., Kvinikadze, G. (1997)

Memoirs on Differential Equations and Mathematical Physics

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Oscillation of certain difference equations

Said R. Grace (2000)

Czechoslovak Mathematical Journal

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Some new criteria for the oscillation of difference equations of the form $Δ^{2} x_{n} - p_{n} Δ x_{n - h} + q_{n} {| x_{g_{n}} |}^{c} s g n x_{g_{n}} = 0$ and $Δ^{i} x_{n} + p_{n} Δ^{i - 1} x_{n - h} + q_{n} {| x_{g_{n}} |}^{c} s g n x_{g_{n}} = 0, i = 2, 3,$ are established.

Oscillation criteria for second order non-linear difference equations

Blażej Szmanda (1983)

Annales Polonici Mathematici

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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.