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Zbl 1165.39307
Liu, Zeqing; Xu, Yuguang; Kang, Shin Min
Global solvability for a second order nonlinear neutral delay difference equation. (English)
[J] Comput. Math. Appl. 57, No. 4, 587-595 (2009). ISSN 0898-1221

Summary: This paper studies the global existence of solutions of the second order nonlinear neutral delay difference equation $$\Delta(a_n\Delta(x_n+bx_{n-\tau}))+f(n,x_{n-d_{1n}},x_{n-d_{2n}},\dots,x_{n-d_{kn}})=c_n,$$ $n\ge n_0$ with respect to all $b\in\bbfR$. A few results on global existence of uncountably many bounded nonoscillatory solutions are established for the above difference equation. Several nontrivial examples which dwell upon the importance of the results obtained in this paper are also included.

MSC 2000:: *39A11 Stability of difference equations
39A10 Difference equations

Keywords: second order nonlinear neutral delay difference equation; uncountably many bounded nonoscillatory solutions; contraction mapping

Cited in: Zbl 1242.39006

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