Oscillatory and Asymptotic Behaviour of Some Difference Equations

A. Sternal; Z. Szafranski; B. Szmanda

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Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations

Ethiraju Thandapani, R. Arul (1999)

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The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form $Δ (a_{n} Δ^{m - 1} y_{n}) + p_{n} Δ^{m - 1} y_{n} + q_{n} f (y_{σ (n + m - 1)}) = 0$ where $m$ is even, is studied. Examples are included to illustrate the results.

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The asymptotic and oscillatory behavior of solutions of Volterra summation equation and second order linear difference equation are studied.

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Mathematica Bohemica

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This paper is concerned with the oscillatory behavior of first-order nonlinear difference equations with variable deviating arguments. The corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term

Bing Gen Zhang, Y. J. Sun (2001)

Mathematica Bohemica

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In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation $Δ (x_{n} - p_{n} x_{τ (n)}) + f (n, x_{σ (n)}) = q_{n}$ are obtained. Examples are included to illustrate the results.

Oscillation criteria for second order non-linear difference equations

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Annales Polonici Mathematici

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