{"paper":{"title":"Existence and bifurcation of solutions for a double coupled system of Schrodinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rushun Tian, Zhitao Zhang","submitted_at":"2015-04-27T04:02:08Z","abstract_excerpt":"Consider the following system of double coupled Schr\\\"odinger equations arising from Bose-Einstein condensates etc.,\n  \\begin{equation*}\n  \\left\\{\\begin{array}{l}\n  -\\Delta u + u =\\mu_1 u^3 + \\beta uv^2- \\kappa v,\n  -\\Delta v + v =\\mu_2 v^3 + \\beta u^2v- \\kappa u,\n  u\\neq0, v\\neq0\\ \\hbox{and}\\ u, v\\in H^1(\\R^N),\n  \\end{array}\n  \\right.\n  \\end{equation*}where $\\mu_1, \\mu_2$ are positive and fixed, $\\kappa$ and $\\beta$ are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06923","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"}