{"paper":{"title":"Fractional semilinear Neumann problems arising from a fractional Keller--Segel model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"B. Volzone, P. R. Stinga","submitted_at":"2014-06-28T14:23:51Z","abstract_excerpt":"We consider the following fractional semilinear Neumann problem on a smooth bounded domain $\\Omega\\subset\\mathbb{R}^n$, $n\\geq2$, $$\\begin{cases} (-\\varepsilon\\Delta)^{1/2}u+u=u^{p},&\\hbox{in}~\\Omega,\\\\ \\partial_\\nu u=0,&\\hbox{on}~\\partial\\Omega,\\\\ u>0,&\\hbox{in}~\\Omega, \\end{cases}$$ where $\\varepsilon>0$ and $1<p<(n+1)/(n-1)$. This is the fractional version of the semilinear Neumann problem studied by Lin--Ni--Takagi in the late 80's. The problem arises by considering steady states of the Keller--Segel model with nonlocal chemical concentration diffusion. Using the semigroup language for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7406","kind":"arxiv","version":4},"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"}