{"paper":{"title":"Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave-convex nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel, Thomas Bartsch","submitted_at":"2015-02-20T16:43:12Z","abstract_excerpt":"We study the bifurcation of solutions of semilinear elliptic boundary value problems of the form \\begin{align*}\n  \\begin{aligned}\n  -\\Delta u &= f_\\lambda(|x|,u,|\\nabla u|) &&\\text{in }\\Omega,\n  u &= 0 &&\\text{on }\\partial\\Omega,\n  \\end{aligned} \\end{align*} on an annulus $\\Omega\\subset\\mathbb{R}^N$, with a concave-convex nonlinearity, a special case being the nonlinearity first considered by Ambrosetti, Brezis and Cerami: $f_\\lambda(|x|,u,|\\nabla u|)=\\lambda|u|^{q-2}u + |u|^{p-2}u$ with $1<q<2<p$. Although the trivial solution $u_0\\equiv0$ is nondegenerate if $\\lambda=0$ we prove that $(\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05927","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"}