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标题：Forced oscillation of higher-order nonlinear neutral difference equations with positive and negative coefficients
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作者：Yali Gao ; Yuangong Sun ; Bin Zha 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：110
DOI：10.1186/1687-1847-2012-110
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the forced oscillation of the higher-order nonlinear difference equation of the form Δ m [ x ( n ) − p ( n ) x ( n − τ ) ] + q 1 ( n ) Φ α ( n − σ 1 ) + q 2 ( n ) Φ β ( n − σ 2 ) = f ( n ) , where m ≥ 1 , τ, σ 1 and σ 2 are integers, 0 0 . By taking all possible values of τ, σ 1 and σ 2 into consideration, we establish some new oscillation criteria for the above equation in two cases: (i) q 1 = q 1 ( n ) ≤ 0 , q 2 = q 2 ( n ) > 0 ; (ii) q 1 ≥ 0 , q 2 < 0 . MSC:39A10.
关键词：forced oscillation ; neutral difference equation ; positive and negative coefficients ; higher-order