Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δ
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Abstract In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δ m ( y n − ∑ j = 1 k p n j y n − m j ) + v n G ( y σ ( n ) ) − u n H ( y α ( n ) ) = f n , $$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive integer and Δ xn = x n+1 − xn . Also we obtain necessary conditions for a particular case of the above equation. We illustrate our results with examples for which it seems no result in the literature can be applied.
1996 ◽
Vol 38
(2)
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pp. 163-171
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2010 ◽
Vol 2010
(1)
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pp. 767620
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2007 ◽
Vol 38
(4)
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pp. 323-333
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2007 ◽
Vol 2007
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pp. 1-16
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