{"paper":{"title":"Existence of solution for a system involving fractional Laplacians and a Radon measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amita Soni, D.Choudhuri","submitted_at":"2019-02-04T13:31:06Z","abstract_excerpt":"An existence of a nontrivial solution in some `weaker' sense of the following system of equations \\begin{align*} (-\\Delta)^{s}u+l(x)\\phi u+w(x)|u|^{k-1}u&=\\mu~\\text{in}~\\Omega\\nonumber\\\\ (-\\Delta)^{s}\\phi&= l(x)u^2~\\text{in}~\\Omega\\nonumber\\\\ u=\\phi&=0 ~\\text{in}~\\mathbb{R}^N\\setminus\\Omega \\end{align*}\n  has been proved. Here $s \\in (0,1)$, $l,w$ are bounded nonnegative functions in $\\Omega$, $\\mu$ is a Radon measure and $k > 1$ belongs to a certain range."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01174","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"}