{"paper":{"title":"On critical $p$-Laplacian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kanishka Perera, Wenming Zou, Zhenyu Guo","submitted_at":"2015-08-25T01:49:35Z","abstract_excerpt":"We consider the critical $p$-Laplacian system \\begin{equation}\\label{92} \\begin{cases}-\\Delta_p u-\\frac{\\lambda a}{p}|u|^{a-2}u|v|^b =\\mu_1|u|^{p^\\ast-2}u+\\frac{\\alpha\\gamma}{p^\\ast}|u|^{\\alpha-2}u|v|^{\\beta}, &x\\in\\Omega,\\\\ -\\Delta_p v-\\frac{\\lambda b}{p}|u|^a|v|^{b-2}v =\\mu_2|v|^{p^\\ast-2}v+\\frac{\\beta\\gamma}{p^\\ast}|u|^{\\alpha}|v|^{\\beta-2}v, &x\\in\\Omega,\\\\ u,v\\ \\text{in } D_0^{1,p}(\\Omega), \\end{cases} \\end{equation} where $\\Delta_p:=\\text{div}(|\\nabla u|^{p-2}\\nabla u)$ is the $p$-Laplacian operator defined on $D^{1,p}(\\mathbb{R}^N):=\\{u\\in L^{p^\\ast}(\\mathbb{R}^N):|\\nabla u|\\in L^p(\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06006","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"}