{"paper":{"title":"Ground states for the double weighted critical Kirchhoff equation on the unit ball in $\\mathbb{R}^3$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiabao Su, Yao Du","submitted_at":"2024-11-02T14:09:22Z","abstract_excerpt":"This paper deals with the existence of ground states for degenerative ($a=0$) and non-degenerative ($a>0$) double weighted critical Kirchhoff equation \\begin{eqnarray*} \\left\\{\n  \\begin{array}{ll} \\displaystyle-\\left(a+b\\int_B |\\nabla u|^2dx\\right)\\Delta u=|x|^{\\alpha_1} |u|^{4+2\\alpha_1}u+\\mu|x|^{\\alpha_2} |u|^{4+2\\alpha_2}u+\\lambda h(|x|) f(u) &{\\rm in}\\ B,\\\\ u=0 &{\\rm on}\\ \\partial B,\n  \\end{array} \\right. \\end{eqnarray*} where $B$ is a unit open ball in $\\mathbb{R}^3$ with center $0$, $a\\geq0, b>0, \\mu\\in \\mathbb{R}, \\lambda>0, \\alpha_1>\\alpha_2>-2$, $4+2\\alpha_i=2^*(\\alpha_i)-2\\ (i=1,2)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01256","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/2411.01256/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"}