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Oscillation and nonoscillation of second order neutral delay difference equations. (English) Zbl 1080.39503
Summary: Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation $\Delta (c_n\Delta (y_n+p_ny_{n-k}))+q_ny_{n+1-m}^\beta =0,\quad n\geq n_0$ where $$k$$, $$m$$ are positive integers and $$\beta$$ is a ratio of odd positive integers are established, under the condition $$\sum \limits _{n=n_0}^{\infty }1/{c_n}<{\infty }$$.

##### MSC:
 39A10 Additive difference equations 39A12 Discrete version of topics in analysis
##### Keywords:
neutral delay; difference equation; oscillation
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##### References:
 [1] R. P. Agarwal: Difference Equations and Inequalities, Secon Edition. Marcel Dekker, New York, 2000. [2] R. P. Agarwal and P. J. Y. Wong: Advanced Topics in Difference Equations. Kluwer Publ., Dordrecht, 1997. · Zbl 0878.39001 [3] D. D. Bainov and D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, 1991. · Zbl 0747.34037 [4] W. T. Li and D. P. Mishev: Classification and existence of positive solutions of second order nonlinear neutral difference equations. Funk. Ekv. 40 (1997), 371-393. [5] B. G. Zhang: Oscillation and asymptotic behavior of second order difference equations. J. Math. Anal. Appl. 173 (1993), 58-68. · Zbl 0780.39006 · doi:10.1006/jmaa.1993.1052
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