{"paper":{"title":"Spikes of the two-component elliptic system in $\\bbr^4$ with Sobolev critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Yuanze Wu","submitted_at":"2018-04-02T05:33:28Z","abstract_excerpt":"Consider the following elliptic system: \\begin{equation*} \\left\\{\\aligned&-\\ve^2\\Delta u_1+\\lambda_1u_1=\\mu_1u_1^3+\\alpha_1u_1^{p-1}+\\beta u_2^2u_1\\quad&\\text{in}\\Omega,\\\\ &-\\ve^2\\Delta u_2+\\lambda_2u_2=\\mu_2u_2^3+\\alpha_2u_2^{p-1}+\\beta u_1^2u_2\\quad&\\text{in}\\Omega,\\\\ &u_1,u_2>0\\quad\\text{in}\\Omega,\\quad u_1=u_2=0\\quad\\text{on}\\partial\\Omega,\\endaligned\\right. \\end{equation*} where $\\Omega\\subset\\bbr^4$ is a bounded domain, $\\lambda_i,\\mu_i,\\alpha_i>0(i=1,2)$ and $\\beta\\not=0$ are constants, $\\ve>0$ is a small parameter and $2<p<2^*=4$. By using the variational method, we study the existence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00400","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"}