Oscillation theorems for second-order advanced functional difference equations. (English) Zbl 0935.39005
The authors obtain some oscillation criteria for the second order difference equation
\[
\Delta\bigl(a(n)\Delta x(n)\bigr)+ p(n)x \bigl(g(n)\bigr)=0
\]
through an appropriate Riccati equation.
Reviewer: E.Thandapani (Salem)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
Keywords:
functional difference equations; oscillation; second order difference equation; Riccati equationReferences:
| [1] | Erbe, L. H.; Zhang, B. G., Oscillation of discrete analogues of delay equations, Diff. and Integral Equations, 2, 300-309 (1989) · Zbl 0723.39004 |
| [2] | Hooker, J.; Patula, W., A second order nonlinear difference equations: Oscillation and asymptotic behavior, J. Math. Anal. Appl., 91, 9-29 (1983) · Zbl 0508.39005 |
| [3] | Patula, W. T., Growth, oscillation properties of second order linear difference equations, SIAM. J. Math. Anal., 10, 1, 55-61 (1979) · Zbl 0397.39001 |
| [4] | Philos, Ch. G., Oscillation in certain difference equations, Utilitas Math., 39, 157-172 (1991) · Zbl 0734.39004 |
| [5] | Patula, W. T., Growth, oscillation and comparison theorems for second order linear difference equations, SIAM. J. Math. Anal., 10, 6, 1272-1279 (1979) · Zbl 0433.39005 |
| [6] | Chen, S. Z.; Erbe, L., Oscillation results for second order scalar and matrix difference equations, Computers Math. Applic., 28, 1-3, 55-69 (1994) · Zbl 0807.39003 |
| [7] | Yan, J., The oscillation properties for the solutions of the second order differential equation with “integral small” coefficient, Acta Math. Sinica, 30, 2, 206-215 (1987) · Zbl 0635.34030 |
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