Oscillation in neutral delay difference equations with variable coefficients. (English) Zbl 0819.39004

Chen, M.-P.; Lalli, B. S.; Yu, J. S.

Comput. Math. Appl. 29, No. 3, 5-11 (1995).

The paper deals with the neutral delay difference equation \[ \Delta (y_ n - p_ n y_{n-k}) + q_ n y_{n-l} = 0, \quad n = 0,1,2, \dots, \] where \(p_ n, q_ n\) \((n=0,1,2, \dots)\) are real numbers with \(p_ n \geq 0\), \(q_ n \geq 0\), \(k\) and \(l\) are nonnegative integers. Some sufficient conditions are established for oscillation of all solutions of the above equation.

Reviewer: A.D.Mednykh (Novosibirsk)

MSC:

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

Keywords:

variable coefficients; neutral delay difference equation; oscillation

References:

[1]	Brayron, R. K.; Willoughby, R. A., On the numerical integration of a symmetric system of difference differential equation of neutral type, J. Math. Anal. Appl., 18, 182-189 (1967) · Zbl 0155.47302
[2]	Georgiou, D. A.; Grove, E. A.; Ladas, G., Oscillation of neutral difference equations, Applicable Analysis, 33, 243-253 (1989) · Zbl 0685.39003
[3]	Georgiou, D. A.; Grove, E. A.; Ladas, G., Oscillation of neutral difference equations with variable coefficients, (Differential Equations: Stability and Control (1990), Marcel Dekker: Marcel Dekker New York), 165-173 · Zbl 0712.39011
[4]	Lalli, B. S.; Zhang, B. G., On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl., 166, 272-287 (1992) · Zbl 0763.39002
[5]	Lalli, B. S.; Zhang, B. G.; Zhao, L. J., On oscillation and existence of positive solutions of neutral difference equations, J. Math. Anal. Appl., 158, 213-233 (1991) · Zbl 0732.39002
[6]	Partheniadis, E. C., Stability and oscillation of neutral delay differential equations with piecewise constant argument, Differential and Integral Equations, 1, 459-472 (1988) · Zbl 0723.34059
[8]	Agarwal, R. P., Difference Equations and Inequalities: Theory, Methods and Applications (1992), Marcel Dekker: Marcel Dekker New York · Zbl 0925.39001
[9]	Kelly, W. G.; Peterson, A. C., Difference Equations, An Introduction with Applications (1991), Academic Press: Academic Press New York
[10]	Lakshmikantham, V.; Trigiante, D., Theory of Difference Equations: Numerical Methods and Applications (1988), Academic Press: Academic Press New York · Zbl 0683.39001
[11]	Yu, J. S.; Chen, M.-P., Oscillations in neutral equations with an “integrably small” coefficient, Internat. J. Math. and Math. Sci., 17, 361-368 (1994) · Zbl 0798.34081