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Keywords:
neutral delay; difference equation; oscillation
neutral delay; difference equation; oscillation
Summary:
Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation \[ \Delta (c_n\Delta (y_n+p_ny_{n-k}))+q_ny_{n+1-m}^\beta =0,\quad n\ge n_0 \] where $k$, $m$ are positive integers and $\beta $ is a ratio of odd positive integers are established, under the condition $\sum _{n=n_0}^{\infty }\frac{1}{c_n}<{\infty }.$
References:
[1] R. P. Agarwal: Difference Equations and Inequalities, Secon Edition. Marcel Dekker, New York, 2000. MR 1740241
[2] R. P. Agarwal and P. J. Y. Wong: Advanced Topics in Difference Equations. Kluwer Publ., Dordrecht, 1997. MR 1447437
[3] D. D. Bainov and D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, 1991. MR 1147908
[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. DOI 10.1006/jmaa.1993.1052 | MR 1205909 | Zbl 0780.39006
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