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Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \\begin{equation*} \\Delta \\left(r_{n}\\left(\\Delta \\left(x_{n}+p_{n}x_{n-k}\\right) \\right) ^{\\gamma}\\right) +q_{n}x_{n}^{\\alpha}+a_{n}f(x_{n})=0. \\end{equation*}% where $x:{\\mathbb{N}}_{0}\\rightarrow {\\mathbb{R}}$, $a,p,q:{\\mathbb{N}}%_{0}\\rightarrow {\\mathbb{R}}$, $r:{\\mathbb{N}}_{0}\\rightarrow {\\mathbb{R}}% \\setminus \\{0\\}$, $f\\colon {\\mathbb{R}}\\rightarrow {\\mathbb{R}}$ is a continuous function, and $k$ is a given positive integer, $\\gamma \\leq 1$ is","authors_text":"Ewa Schmeidel, Magdalena Nockowska Rosiak, Marek Galewski, Robert Jankowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-09T09:30:54Z","title":"On the existence of bounded solutions for nonlinear second order neutral difference 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