Displaying similar documents to “Oscillation criteria for first-order forced nonlinear difference equations.”

An improved oscillation theorem for nonlinear differential equations of advanced type

Nurten Kiliç, Özkan Öcalan, Mustafa Kemal Yildiz (2024)

Archivum Mathematicum

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This paper deals with the oscillatory solutions of the first order nonlinear advanced differential equation. The aim of the present paper is to obtain an oscillation condition for this equation. This result is new and improves and correlates many of the well-known oscillation criteria that were in the literature. Finally, an example is given to illustrate the main result.

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.