{"paper":{"title":"Semilinear nonlocal elliptic equations with critical and supercritical exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta","submitted_at":"2016-08-27T03:09:00Z","abstract_excerpt":"We study the problem \\begin{eqnarray*} (-\\Delta)^s u &=& u^p - u^q \\quad\\text{in }\\quad \\mathbb{R}^N, u &\\in& \\dot{H}^s(\\mathbb{R}^N)\\cap L^{q+1}(\\mathbb{R}^N), u&>0& \\quad\\text{in}\\quad\\mathbb{R}^N, \\end{eqnarray*} where $s\\in(0,1)$ is a fixed parameter, $(-\\Delta)^s$ is the fractional laplacian in $\\mathbb{R}^N$, $q>p\\geq \\frac{N+2s}{N-2s}$ and $N>2s$. For every $s\\in(0,1)$, we establish regularity results of solutions of above equation (whenever solution exists) and we show that every solution is a classical solution. Next, we derive certain decay estimate of solutions and the gradient of s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07654","kind":"arxiv","version":7},"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"}