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We prove that there exists an equivariant solution u(x_1, x_2) satisfying u(x_1, x_2) -> a^\\pm, as x_1 -> \\pminfiniti, and u(x_1, x_2) -> e^\\pm(x_1), as x_2 -> \\pminfiniti. The problem above was first studied by Alama, Bronsard, and Gui under related hypotheses to the ones introduced in the present paper. At the expense of one extra sy"},"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":"0810.5009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-28T11:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"67447ab6039aa54898ed9ab33ba3e500c31255f50110ebd2f4e1c1f60c4b5107","abstract_canon_sha256":"44b5ef053b57d5dee7127a8d22c8d4a7cafeec4154350cc291854180d0599129"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:15.698451Z","signature_b64":"4+6BKviAQOez3yktR+sZn+V45Pf0x7A0+YfeXmy213M+d33wpzn0KSLtwOc3tMNemqpD9CE0jtz5yz/M9l1QDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d5637afef6bb61c85aec41444a2ecab7d591e80e37bc651f21c64c53f222790","last_reissued_at":"2026-05-18T04:38:15.697813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:15.697813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On an elliptic system with symmetric potential possessing two global minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giorgio Fusco, Nicholas D. Alikakos","submitted_at":"2008-10-28T11:46:58Z","abstract_excerpt":"We consider the system {\\Delta}u - W_u (u) = 0, for u: R^2 -> R^2, W: R^2 -> R, where W_u (u) is a smooth potential, symmetric with respect to the u_1, u_2 axes, possessing two global minima a^\\pm := (\\pma,0) and two connections e^\\pm(x_1) connecting the minima. We prove that there exists an equivariant solution u(x_1, x_2) satisfying u(x_1, x_2) -> a^\\pm, as x_1 -> \\pminfiniti, and u(x_1, x_2) -> e^\\pm(x_1), as x_2 -> \\pminfiniti. The problem above was first studied by Alama, Bronsard, and Gui under related hypotheses to the ones introduced in the present paper. 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