{"paper":{"title":"Semi-linear cooperative elliptic systems involving Schr{\\\"o}dinger operators: Groundstate positivity or negativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B\\'en\\'edicte Alziary, Jacqueline Fleckinger (IMT)","submitted_at":"2019-01-11T08:29:09Z","abstract_excerpt":"We study here the behavior  of the solutions to a $2\\times 2$  semi-linear cooperative  system involving Schr\\\" odinger operators (considered in its variational form): $$LU:=(-\\Delta + q(x))U = AU+\\mu U + F(x,U) \\quad{\\rm in}\\ \\mathbb{R}^N$$ $$U(x)_{|x|\\rightarrow \\infty} \\rightarrow 0$$ where $q$ is a continuous  positive potential tending to $+\\infty$ at infinity; $\\mu$ is a real parameter varying near the principal eigenvalue of the system; $U$ is a column vector with components $u_1$ and $u_2$ and $A$ is a square cooperative  matrix with constant  coefficient. $F$ is a column vector with c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03505","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"}