{"paper":{"title":"Critical exponent for half-Laplacian in the whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Pawan Mishra","submitted_at":"2015-10-03T10:04:12Z","abstract_excerpt":"We study the existence of {weak} solutions for fractional elliptic equations of the type, \\begin{equation*} (-\\Delta)^{\\frac{1}{2}} u+ V(x) u= h(u), u> 0 \\;\\textrm{in} \\;\\mathbb R, \\end{equation*} %where $1<q<2,\\;p>2,\\;1<\\beta\\leq2\\;, \\lambda>0, K(x)>0, f$ is continuous and sign changing. where $h$ is a real valued function that behaves like $e^{u^2}$ as $u\\rightarrow \\infty$ and $V(x)$ is a positive, continuous unbounded function. Here $(-\\Delta)^{\\frac{1}{2}}$ is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near $t=0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00804","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"}