{"paper":{"title":"Nonlinear three point Singular BVPs : A Classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Amit K. Verma, Mandeep Singh","submitted_at":"2015-08-29T06:19:35Z","abstract_excerpt":"We analyze the existence of unique solutions of the following class of nonlinear three point singular boundary value problems (SBVPs), \\begin{eqnarray*}\\label{NL-Singular-P} &&-(x^{\\alpha} y'(x))'= x^{\\alpha}f(x,y),\\quad 0<x<1,\\\\ &&y'(0)=0,\\quad y(1)=\\delta y(\\eta), \\end{eqnarray*} where $\\delta>0$, $0<\\eta<1$ and $\\alpha \\geq 1$. This study shows some novel observations regarding the nature of the solution of the nonlinear three point SBVPs. We observe that when $sup\\left(\\partial f/\\partial y\\right)>0$ for $\\alpha\\in \\cup_{n\\in \\mathbb{N}}\\left(4n-1,4n+1\\right)$ or $\\alpha\\in\\{1,5,9,\\cdots\\}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07408","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"}