Oscillation for higher-order neutral superlinear delay difference equations with unstable type. (English) Zbl 1089.39002

Lin, Xiaoyan

Comput. Math. Appl. 50, No. 5-6, 683-691 (2005).

This paper offers some criteria for the existence of an unbounded/bounded positive solution of even-order neutral superlinear delay difference equations of the type \[ \Delta^m(x_n-p_nx_{n-\tau})=q_nx^\alpha_{n-\sigma}. \]

Reviewer: Mingshu Peng (Beijing)

MSC:

39A11	Stability of difference equations (MSC2000)
39A12	Discrete version of topics in analysis
34K11	Oscillation theory of functional-differential equations

Keywords:

oscillation; nonoscillation; positive solution; neutral superlinear delay difference equations

References:

[1]	Lalli, B. S.; Zhang, B. G., On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl., 166, 272-287 (1992) · Zbl 0763.39002
[2]	Shen, J. H., On second order neutral delay difference equations with variable coefficients, Journal of Mathematical Study, 27, 60-70 (1994) · Zbl 0917.39006
[3]	Lin, X. Y.; Shen, J. H., Bounded oscillation for a class of even order neutral difference equations, Fasciculi Mathematici, 33, 37-47 (2002) · Zbl 1034.39006
[4]	Tang, X. H.; Liu, Y. J., Oscillation for nonlinear delay difference equations, Tamkang Journal of Mathematics, 32, 4, 275-280 (2001) · Zbl 1007.39003
[5]	Agarwal, R. P., Difference Equations and Inequalities (1992), Marcel Dekker: Marcel Dekker Berlin · Zbl 0784.33008
[6]	Zhang, G.; Gao, Y., Oscillation Theory of Difference Equations (2000), Publishing House of Higher Education: Publishing House of Higher Education New York
[7]	Györi, I.; Ladas, G., Oscillation Theory of Delay Differential Equations With Applications (1991), Clarendon Press · Zbl 0780.34048
[8]	Tang, X. H.; Yu, J. S.; Peng, D. H., Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients, Computers Math. Applic., 39, 7/8, 169-181 (2000) · Zbl 0958.39016
[9]	Tang, X. H.; Yu, J. S., Oscillation of delay difference equations, Computers Math. Applic., 37, 7, 11-20 (1999) · Zbl 0937.39012
[10]	Tang, X. H.; Yu, J. S., Oscillation of delay difference equations, Hokkaido Mathematical. J., 29, 213-228 (2000) · Zbl 0958.39015