{"paper":{"title":"Multiple positive solutions to elliptic boundary blow-up problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Boscaggin, Duccio Papini, Walter Dambrosio","submitted_at":"2016-07-19T14:01:35Z","abstract_excerpt":"We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem \\[ \\left\\{\\begin{array}{ll} \\Delta u + \\bigl(a^+(\\vert x \\vert) - \\mu a^-(\\vert x \\vert)\\bigr) g(u) = 0, & \\; \\vert x \\vert < 1, \\\\ u(x) \\to \\infty, & \\; \\vert x \\vert \\to 1, \\end{array} \\right. \\] where $g$ is a function superlinear at zero and at infinity, $a^+$ and $a^-$ are the positive/negative part, respectively, of a sign-changing function $a$ and $\\mu > 0$ is a large parameter. In particular, we show how the number of solutions is affected by the nodal behavior of the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05585","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"}