{"paper":{"title":"Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniele Cassani, Hugo Tavares, Jianjun Zhang","submitted_at":"2018-10-10T13:36:30Z","abstract_excerpt":"We prove, using variational methods, the existence in dimension two of positive vector ground states solutions for the Bose-Einstein type systems \\begin{equation} \\begin{cases} -\\Delta u+\\lambda_1u=\\mu_1u(e^{u^2}-1)+\\beta v\\left(e^{uv}-1\\right) \\text{ in } \\Omega, &\\\\ -\\Delta v+\\lambda_2v=\\mu_2v(e^{v^2}-1)+\\beta u\\left(e^{uv}-1\\right)\\text{ in } \\Omega, &\\\\ u,v\\in H^1_0(\\Omega) \\end{cases} \\end{equation} where $\\Omega$ is a bounded smooth domain, $\\lambda_1,\\lambda_2>-\\Lambda_1$ (the first eigenvalue of $(-\\Delta,H^1_0(\\Omega))$, $\\mu_1,\\mu_2>0$ and $\\beta$ is either positive (small or large) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04524","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"}