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We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the po"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.06923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-27T04:02:08Z","cross_cats_sorted":[],"title_canon_sha256":"fbbc0a3f7f1e003506f873891d28876f0f2e58bdfbe3d7c120e1425d9ca1423e","abstract_canon_sha256":"82d4d1cd067c27453188e40bcdf239e0e012b5ec5085eabb645dd3d4d25760ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:44.091481Z","signature_b64":"iM2Dh42/YW3OV7AHJtYsxOTMIwO87U1vIgfW7ZS9dZ2bbzQbTMq0eyDjpxfCmZAr/EgRS2LZD+JZc6HrUFF3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad2a5886e495a15378461d5794aeface0cb4c1d134dd6d616994cbe03a12782f","last_reissued_at":"2026-05-18T02:17:44.091109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:44.091109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and bifurcation of solutions for a double coupled system of Schrodinger 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. 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