Oscillation and nonoscillation of second order neutral delay difference equations. (English) Zbl 1080.39503

Thandapani, E.; Mahalingam, K.

Czech. Math. J. 53, No. 4, 935-947 (2003).

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

References:

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[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