{"paper":{"title":"A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J\\'ozsef Szabados, Paul Nevai, Saud M. Alsulami, Walter Van Assche","submitted_at":"2013-12-09T10:29:41Z","abstract_excerpt":"We study solutions $(x_n)_{n \\in \\mathbb{N}}$ of nonhomogeneous nonlinear second order difference equations of the type $\\ell_n = x_n ( \\sigma_{n,1} x_{n+1} + \\sigma_{n,0} x_n + \\sigma_{n,-1} x_{n-1} ) + \\kappa_n x_n$, with given initial data $x_0 \\in \\mathbb{R}$, $x_1 \\in \\mathbb{R}^+$ where $(\\ell_n)_{n\\in\\mathbb{N}} \\in \\mathbb{R}^+$, $(\\sigma_{n,0})_{n\\in\\mathbb{N}} \\in \\mathbb{R}^+$ and $(\\kappa_n)_{n\\in\\mathbb{N}} \\in \\mathbb{R}$ and the left and right $\\sigma$-coefficients satisfy either $(\\sigma_{n,1})_{n\\in\\mathbb{N}} \\in \\mathbb{R}^+$ and $(\\sigma_{n,-1})_{n\\in \\mathbb{N}} \\in \\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2370","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"}