{"paper":{"title":"Positive solutions for nonlinear Choquard equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konijeti Sreenadh, Tuhina Mukherjee","submitted_at":"2016-09-23T08:51:47Z","abstract_excerpt":"In this article, we study the following nonlinear Choquard equation with singular nonlinearity \\begin{equation*}\n  \\quad -\\De u = \\la u^{-q} + \\left( \\int_{\\Om}\\frac{|u|^{2^*_{\\mu}}}{|x-y|^{\\mu}}\\mathrm{d}y \\right)|u|^{2^*_{\\mu}-2}u, \\quad u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{on}\\; \\partial\\Om, \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > 2,\\; \\la >0,\\; 0 < q < 1, \\; 0<\\mu<n$ and $2^*_\\mu=\\frac{2n-\\mu}{n-2}$. Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07273","kind":"arxiv","version":2},"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"}