{"paper":{"title":"Multiple positive solutions of the stationary Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benedetta Noris, Denis Bonheure, Jean-Baptiste Casteras","submitted_at":"2016-03-23T21:43:12Z","abstract_excerpt":"We consider the stationary Keller-Segel equation \\begin{equation*} \\begin{cases} -\\Delta v+v=\\lambda e^v, \\quad v>0 \\quad & \\text{in }\\Omega,\\\\ \\partial_\\nu v=0 &\\text{on } \\partial \\Omega, \\end{cases} \\end{equation*} where $\\Omega$ is a ball. In the regime $\\lambda\\to 0$, we study the radial bifurcations and we construct radial solutions by a gluing variational method. For any given natural positive number $n$, we build a solution having multiple layers at $r_1,\\ldots,r_n$ by which we mean that the solutions concentrate on the spheres of radii $r_i$ as $\\lambda\\to 0$ (for all $i=1,\\ldots,n$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07374","kind":"arxiv","version":1},"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"}