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

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.

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.