{"paper":{"title":"Concentrating phenomenon for fractional nonlinear Schr\\\"{o}dinger-Poisson system with critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaimin Teng","submitted_at":"2019-06-27T11:43:31Z","abstract_excerpt":"In this paper, we study the following fractional Schr\\\"{o}dinger-Poisson system \\begin{equation*} \\left\\{\n  \\begin{array}{ll}\n  \\varepsilon^{2s}(-\\Delta)^su+V(x)u+\\phi u=g(u) & \\hbox{in $\\mathbb{R}^3$,}\n  \\varepsilon^{2t}(-\\Delta)^t\\phi=u^2,\\,\\, u>0& \\hbox{in $\\mathbb{R}^3$,}\n  \\end{array} \\right. \\end{equation*} where $s,t\\in(0,1)$, $\\varepsilon>0$ is a small parameter. Under some suitable assumptions on potential function $V(x)$ and critical nonlinearity term $g(u)$, we construct a family of positive solutions $u_{\\varepsilon}\\in H^s(\\mathbb{R}^3)$ which concentrates around the global minima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11563","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"}