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Moreover, we assume that"},"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":"1708.00457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-01T18:02:01Z","cross_cats_sorted":[],"title_canon_sha256":"9a244e25b8d348ffb227816dbbd27efafc17fe1bfaa79361415db40d7ec6c04b","abstract_canon_sha256":"b0f8abeb60eff675b5eac90f050bafb3b0c0b09165676b9afd06ebd0b135408d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:47.119557Z","signature_b64":"jN0neA+xLvYfITa5TkjGcXyk9nPy/SYpsgyuRjtMzpuldQDXAOmOVzCxXwRPiK0D2KR0kBZY7+vF6cIfk+CnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe873697800b86dcf4e79537ff1fa3aacab7d00dff9737b329b91b2d51686e80","last_reissued_at":"2026-05-18T00:38:47.118804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:47.118804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupled elliptic systems involving the square root of the Laplacian and Trudinger-Moser critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","submitted_at":"2017-08-01T18:02:01Z","abstract_excerpt":"In this paper we prove the existence of a nonnegative ground state solution to the following class of coupled systems involving Schr\\\"{o}dinger equations with square root of the Laplacian\n  $$\n  \\left\\{\n  \\begin{array}{lr}\n  (-\\Delta)^{1/2}u+V_{1}(x)u=f_{1}(u)+\\lambda(x)v, & x\\in\\mathbb{R},\n  (-\\Delta)^{1/2}v+V_{2}(x)v=f_{2}(v)+\\lambda(x)u, & x\\in\\mathbb{R},\n  \\end{array}\n  \\right.\n  $$\n  where the nonlinearities $f_{1}(s)$ and $f_{2}(s)$ have exponential critical growth of the Trudinger-Moser type, the potentials $V_{1}(x)$ and $V_{2}(x)$ are nonnegative and periodic. 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