{"paper":{"title":"Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John A. Pelesko, Nicholas D. Brubaker","submitted_at":"2012-01-26T02:34:02Z","abstract_excerpt":"In this paper we analyze the classical solution set ({\\lambda},u), for {\\lambda}>0, of a one-dimensional prescribed mean curvature equation on the interval [-L,L]. It is shown that the solution set depends on the two parameters, {\\lambda} and L, and undergoes two bifurcations. The first is a standard saddle node bifurcation, which happens for all L at {\\lambda} = {\\lambda}*(L). The second is a splitting bifurcation; specifically, there exists a value L* such that as L transitions from greater than or equal L* to less than L* the upper branch of the bifurcation diagram splits into two parts. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5432","kind":"arxiv","version":3},"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"}