{"paper":{"title":"Classification of nonnegative solutions to static Schr\\\"{o}dinger-Hartree-Maxwell type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guolin Qin, Wei Dai, Zhao Liu","submitted_at":"2019-09-01T23:45:37Z","abstract_excerpt":"In this paper, we are mainly concerned with the physically interesting static Schr\\\"{o}dinger-Hartree-Maxwell type equations \\begin{equation*}\n  (-\\Delta)^{s}u(x)=\\left(\\frac{1}{|x|^{\\sigma}}\\ast |u|^{p}\\right)u^{q}(x) \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\text{in} \\,\\,\\, \\mathbb{R}^{n} \\end{equation*} involving higher-order or higher-order fractional Laplacians, where $n\\geq1$, $0<s:=m+\\frac{\\alpha}{2}<\\frac{n}{2}$, $m\\geq0$ is an integer, $0<\\alpha\\leq2$, $0<\\sigma<n$, $0<p\\leq\\frac{2n-\\sigma}{n-2s}$ and $0<q\\leq\\frac{n+2s-\\sigma}{n-2s}$. We first prove the super poly-harmonic properties of nonnegative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00492","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00492/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}