Oscillatory mixed difference systems.

Ferreira, José M.; Pinelas, Sandra

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Frequent oscillatory behavior of delay partial difference equations with positive and negative coefficients.

Xu, Li Hua, Yang, Jun (2010)

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Variational oscillation criteria for nonlinear nonhomogeneous differential equations.

Zheng, Zhaowen, Cheng, Sui Sun (2007)

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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).