{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7WS6DFFEU3QRCCKXGXGDHM4YTM","short_pith_number":"pith:7WS6DFFE","schema_version":"1.0","canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","source":{"kind":"arxiv","id":"1212.3773","version":2},"attestation_state":"computed","paper":{"title":"Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system","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":"2012-12-16T10:44:45Z","abstract_excerpt":"We study the following coupled Schr\\\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {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 \\,$\\partial\\Om$}.{cases}{displaymath} Here $\\Om$ is a smooth bounded domain in $\\R^N (N=2, 3)$ or $\\Om=\\RN$, $\\la_1,\\, \\la_2$, $\\mu_1,\\,\\mu_2$ are all positive constants and the coupling constant $\\bb<0$. We show that this system has infinitely many sign-changing solutions. We also obtain "},"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":"1212.3773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-16T10:44:45Z","cross_cats_sorted":[],"title_canon_sha256":"35264144da404aba99df2ad01bea6795abf60603b86656dcbeb61b1fc6da857d","abstract_canon_sha256":"cf5ec9a3d4a89021ca413663deee27e93fb4b8167e8b28134672e9cbaaf617c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:06.268384Z","signature_b64":"/1wtSuTSRLuaOVSbA1Jg9TdJ0gHy0lC9v/6UX3eZrbOxKGSKmLZFKZYGV0yDgqvSfaWVcuTPdtnCqGiq3W0IAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fda5e194a4a6e111095735cc33b3989b13a68fc7ec74f797ea51e916f1ff5f20","last_reissued_at":"2026-05-18T02:42:06.267901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:06.267901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system","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":"2012-12-16T10:44:45Z","abstract_excerpt":"We study the following coupled Schr\\\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {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 \\,$\\partial\\Om$}.{cases}{displaymath} Here $\\Om$ is a smooth bounded domain in $\\R^N (N=2, 3)$ or $\\Om=\\RN$, $\\la_1,\\, \\la_2$, $\\mu_1,\\,\\mu_2$ are all positive constants and the coupling constant $\\bb<0$. We show that this system has infinitely many sign-changing solutions. 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