{"paper":{"title":"Elliptic Problems in $\\mathbb{R}^N$ with Critical and Singular Discontinuous Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, R. Dhanya, S. Prashanth, Sweta Tiwari","submitted_at":"2016-06-04T11:26:05Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb R^{N}$, $N\\geq3$ with smooth boundary,\n  $a>0, \\lambda>0$ and $0<\\delta<3$ be real numbers. Define $2^*:=\\displaystyle\\frac{2N}{N-2}$ and the characteristic function of a set $A$ by $\\chi_A$.\n  We consider the following critical problem with singular and discontinuous nonlinearity: \\begin{eqnarray*}\n  (P_\\la^a)~~~~ \\qquad \\Biggl\\{\\begin{array}{rl} -\\Delta u &= \\lambda \\left(u^{2^*-1}+ \\displaystyle \\chi_{\\{u<a\\}}u^{-\\de} \\right), u > 0~~\\text{in} ~~\\Omega, \\\\ u & = 0 ~\\text{on}~\n  \\partial \\Omega. \\end{array} \\end{eqnarray*}\n  \\noindent We study the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01370","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"}