{"paper":{"title":"On the existence of bounded solutions for nonlinear second order neutral difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ewa Schmeidel, Magdalena Nockowska Rosiak, Marek Galewski, Robert Jankowski","submitted_at":"2013-04-09T09:30:54Z","abstract_excerpt":"\\noindent 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2501","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}