{"paper":{"title":"Nonexistence of anti-symmetric solutions for fractional Hardy-H\\'{e}non System","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiaqi Hu, Zhuoran Du","submitted_at":"2022-11-14T03:17:22Z","abstract_excerpt":"We study anti-symmetric solutions about the hyperplane $\\{x_n=0\\}$ to the following fractional Hardy-H\\'{e}non system $$ \\left\\{\\begin{aligned} &(-\\Delta)^{s_1}u(x)=|x|^\\alpha v^p(x),\\ \\ x\\in\\mathbb{R}_+^n, \\\\&(-\\Delta)^{s_2}v(x)=|x|^\\beta u^q(x),\\ \\ x\\in\\mathbb{R}_+^n, \\\\&u(x)\\geq 0,\\ \\ v(x)\\geq 0,\\ \\ x\\in\\mathbb{R}_+^n, \\end{aligned}\\right. $$ where $0<s_1,s_2<1$, $n>2\\max\\{s_1,s_2\\}$. Nonexistence of anti-symmetric solutions are obtained in some appropriate domains of $(p,q)$ under some corresponding assumptions of $\\alpha,\\beta$ via the methods of moving spheres and moving planes. Particul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07081","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.07081/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"}