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We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $\\mu_1,\\mu_2, p, \\beta$. We als"},"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":"1705.09100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-25T09:20:31Z","cross_cats_sorted":[],"title_canon_sha256":"8aed995e34767d8b05e572f6b4721e3c160f4b423dba8489bb14d8b4eb3f3497","abstract_canon_sha256":"411b67fd2c51c45017fe5c8b8ae77667b573c60ecba639cae9778142e2d11360"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:40.424815Z","signature_b64":"1nl+7a/3B1QCpJ3yApkFZD4WQYznEInTX+70aMBbcCJJEeTavJFz7KkXbnHTrVzavX/L2LJqvnejUJ/ml2oWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a340c3f2e694d899633ec014e5dbaacb7cacd7fa67414379b1b5752166da8972","last_reissued_at":"2026-05-18T00:43:40.424270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:40.424270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qihan He, Shuangjie Peng, Yan-fang Peng","submitted_at":"2017-05-25T09:20:31Z","abstract_excerpt":"In this paper, we study the following fractional nonlinear Schr\\\"odinger system $$ \\left\\{% \\begin{array}{ll} (-\\Delta)^s u +u=\\mu_1 |u|^{2p-2}u+\\beta |v|^p|u|^{p-2}u,~~x\\in \\R^N,\\vspace{2mm}\\\\ (-\\Delta)^s v +v=\\mu_2 |v|^{2p-2}v+\\beta |u|^p|v|^{p-2}v,~~x\\in \\R^N, \\end{array}% \\right. $$ where $0<s<1, \\mu_1 >0, \\mu_2>0, 1<p<2_s^*/2, 2_s^*=+\\infty$ for $N\\le 2s$ and $2_s^*=2N/(N-2s)$ for $N>2s$, and $\\beta \\in \\R$ is a coupling constant. We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $\\mu_1,\\mu_2, p, \\beta$. 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