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Global solvability for a second order nonlinear neutral delay difference equation. (English) Zbl 1165.39307

Summary: This paper studies the global existence of solutions of the second order nonlinear neutral delay difference equation

${\Delta }\left({a}_{n}{\Delta }\left({x}_{n}+b{x}_{n-\tau }\right)\right)+f\left(n,{x}_{n-{d}_{1n}},{x}_{n-{d}_{2n}},\cdots ,{x}_{n-{d}_{kn}}\right)={c}_{n},$

$n\ge {n}_{0}$ with respect to all $b\in ℝ$. 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:
 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations
##### References:
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