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Oscillations of neutral difference equations. (English) Zbl 0685.39003

Consider the difference equation \((1)\quad \Delta (y_ n+py_{n- k})+qy_{n-\ell}=0,\quad n=0,1,2,...,\) where p and q are real numbers, k and \(\ell\) are integers and \(\Delta\) denotes the forward difference operator \(\Delta x_ n=x_{n+1}-x_ n.\) The authors obtain sufficient conditions for the oscillation of all solutions of the difference equation (1).
Reviewer: B.G.Pachpatta

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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References:

[1] Erbe, L. H. and Zhang, B.G. 1988.Oscillation of discrete analogues of delay equations, Proceedings of the International Conference on Theory and Applications of Differential Equations, 21–25. to be published by Marcel Dekker, Inc.
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[3] Gyori I., Linearized oscillations for equations with piecewise constant arguments, Differential and Integral Equation
[4] Ladas, G. 1988.Oscillations of equations with piecewise constant arguments, Proceedings of the International Conference on Theory and Applications of Differential Equations, 21–25. Oscillations of equations with piecewise constant arguments, Proceedings of the International Conference on Theory and Applications of Differential Equations.
[5] Ladas G., Sharp conditions for the oscillation of delay difference equations · Zbl 0685.39004
[6] Ladas G., Canad. Math. Bull 24 (1989)
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