Oscillation of second order nonlinear neutral delay difference equations. (English) Zbl 1035.34074
Summary: We obtain sufficient conditions for the oscillation of all solutions to the second-order nonlinear delay difference equation
\[
\Delta[a_n(\Delta(x_n+p_nx_{g(n)}))^{\alpha}]+f(n,x_{\sigma(n)})=0,
\]
where \(\Delta x_n=x_{n+1}-x_n\) is the forward difference operator, \(\{p_n\}\) is a sequence of nonnegative real numbers and \(\alpha \geqslant 1\) is a quotient of positive odd integers. Our results extend and improve some known results in the literature. An example that dwell up the advantage of our results is included.
MSC:
34K11 | Oscillation theory of functional-differential equations |
34K40 | Neutral functional-differential equations |
References:
[1] | Jiang, J. C., Oscillatory criteria for second-order quasilinear neutral delay difference equations, Appl. Math. Comput., 125, 287-293 (2002) · Zbl 1030.39009 |
[2] | Szafranski, Z.; Szmand, B., Oscillation theorems for some nonlinear difference equations, Appl. Math. Comput., 83, 43-52 (1997) · Zbl 0871.39006 |
[3] | Luo, J. W., Oscillation criteria for second order neutral difference equations, Ann. Diff. Eqs., 14, 262-266 (1998) · Zbl 0963.39013 |
[4] | Jiang, J. C.; Li, X. P., Oscillatory and asymptotic behavior for second order quasilinear difference equations, Northeast. Math. J., 17, 315-322 (2001) · Zbl 1029.39012 |
[5] | Agarwal, R. P., Difference Equations and Inequalities, Theory Methods and Applications (1992), Marcel Deker: Marcel Deker New York · Zbl 0925.39001 |
[6] | Kelly, W. G.; Peterson, A. C., Difference Equations, an Introduction with Application (1991), Acadamic Press Inc: Acadamic Press Inc Boston, MA · Zbl 0733.39001 |
[7] | Jiang, J. C.; Li, X. P., Oscillation of second order nonlinear neutral differential equations, Appl. Math. Comput., 135, 531-540 (2003) · Zbl 1026.34081 |
[8] | Li, H.; Liu, W., Oscillation criteria for second order neutral differential equations, Can. J. Math., 48, 871-886 (1996) · Zbl 0859.34055 |
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