{"paper":{"title":"Profile of solutions for nonlocal equations with critical and supercritical nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta, Sanjiban Santra","submitted_at":"2016-12-06T11:24:26Z","abstract_excerpt":"We study the fractional laplacian problem (-\\Delta)^s u &=& u^p -\\epsilon u^q \\quad\\text{in }\\quad \\Omega, u &\\in& H^s(\\Omega)\\cap L^{q+1}(\\Omega),u &>&0 \\quad\\text{in }\\quad \\Omega, u&=&0 \\quad\\text{in}\\quad \\mathbb{R}^N\\setminus\\Omega, where $s\\in(0,1)$, $q>p\\geq \\frac{N+2s}{N-2s}$ and $\\epsilon>0$ is a parameter. Here $\\Omega\\subseteq\\mathbb{R}^N$ is a bounded star-shaped domain with smooth boundary and $N> 2 s$. We establish existence of a variational positive solution $u_{\\epsilon}$ and characterize the asymptotic behaviour of $u_{\\epsilon}$ as $\\epsilon\\to 0$. When $p=\\frac{N+2s}{N-2s}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01759","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"}