{"paper":{"title":"Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Wenming Zou, Zhijie Chen","submitted_at":"2013-04-18T06:26:37Z","abstract_excerpt":"We study the following coupled Schr\\\"{o}dinger equations which have appeared as several models from mathematical physics: \\begin{displaymath} \\begin{cases}-\\Delta u_1 +\\la_1 u_1 = \\mu_1 u_1^3+\\beta u_1 u_2^2, \\quad x\\in \\Omega,\\\\ -\\Delta u_2 +\\la_2 u_2 =\\mu_2 u_2^3+\\beta u_1^2 u_2, \\quad x\\in \\Om,\\\\ u_1=u_2=0 \\,\\,\\,\\hbox{on \\,$\\partial\\Om$}.\\end{cases}\\end{displaymath} Here $\\Om\\subset\\RN (N=2, 3)$ is a smooth bounded domain, $\\la_1, \\la_2$, $\\mu_1, \\mu_2$ are all positive constants. We show that, for each $k\\in\\mathbb{N}$ there exists $\\bb_k>0$ such that this system has at least $k$ sign-chan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5030","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"}