Half-linear discrete oscillation theory.

Řehák, Pavel

Displaying similar documents to “Half-linear discrete oscillation theory.”

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

Došlý, Ondřej, Fišnarová, Simona (2008)

Advances in Difference Equations [electronic only]

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

Zdeněk Opluštil (2014)

Mathematica Bohemica

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Oscillatory properties of solutions to the system of first-order linear difference equations $\begin{matrix} Δ u_{k} & = q_{k} v_{k} \\ Δ v_{k} & = - p_{k} u_{k + 1}, \end{matrix}$ are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).

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.