{"paper":{"title":"Standing waves for two-component elliptic system with critical growth in $\\mathbb{R}^{4}$: the attractive case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lun Guo, Qi Li, Riccardo Molle, Xiao Luo","submitted_at":"2022-11-07T10:28:23Z","abstract_excerpt":"In this paper, we consider the following two-component elliptic system with critical growth \\begin{equation*}\n  \\begin{cases}\n  -\\Delta u+(V_1(x)+\\lambda)u=\\mu_1u^{3}+\\beta uv^{2}, \\ \\ x\\in \\mathbb{R}^4,\n  -\\Delta v+(V_2(x)+\\lambda)v=\\mu_2v^{3}+\\beta vu^{2}, \\ \\ x\\in \\mathbb{R}^4 ,\n  % u\\geq 0, \\ \\ v\\geq 0 \\ \\text{in} \\ \\R^4.\n  \\end{cases} \\end{equation*} where $V_j(x) \\in L^{2}(\\mathbb{R}^4)$ are nonnegative potentials and the nonlinear coefficients $\\beta ,\\mu_j$, $j=1,2$, are positive. Here we also assume $\\lambda>0$. By variational methods combined with degree theory, we prove some results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.03425","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/2211.03425/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"}