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Here the coefficient $\\lambda(x)$ of the coupling term is related with the potentials by the condition $|\\lambda(x)|\\leq\\delta a(x)^{\\alpha/p}b(x)^{\\beta/q}$ where $\\delta\\in(0,1)$ and $\\"},"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":"1709.09709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-27T19:33:12Z","cross_cats_sorted":[],"title_canon_sha256":"f9a7834e55b3336b6d7516b58f9120f2f8e6c9112667a60dfe92b01f06b62b60","abstract_canon_sha256":"187535f4eb7dca9a5c24891c69e8788185d7a3857178b9529d53730bf242070a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:28.769950Z","signature_b64":"NmP/HOVdlPdBSNB3icRDMILVTyjdZbrqB2Yvqg3bruNmxX2kXDUs1GHZdTdzkoGyWkDqd/LOChFLadoqoDhBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d946a0ec59679df5b6ada97a4193e75a4367e0e8625d3153d7dfb7fa98dc9d9","last_reissued_at":"2026-05-18T00:25:28.769263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:28.769263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive ground states for a class of superlinear $(p,q)$-Laplacian coupled systems involving Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edcarlos Domingos da Silva, Jo\\~ao Marcos do \\'O, Jos\\'e Carlos de Albuquerque","submitted_at":"2017-09-27T19:33:12Z","abstract_excerpt":"We study the existence of positive solutions for the following class of $(p,q)$-Laplacian coupled systems\n  \\[\n  \\left\\{\n  \\begin{array}{lr}\n  -\\Delta_{p} u+a(x)|u|^{p-2}u=f(u)+ \\alpha\\lambda(x)|u|^{\\alpha-2}u|v|^{\\beta}, & x\\in\\mathbb{R}^{N},\n  -\\Delta_{q} v+b(x)|v|^{q-2}v=g(v)+ \\beta\\lambda(x)|v|^{\\beta-2}v|u|^{\\alpha}, & x\\in\\mathbb{R}^{N},\n  \\end{array}\n  \\right.\n  \\] where $N\\geq3$ and $1\\leq p\\leq q<N$. Here the coefficient $\\lambda(x)$ of the coupling term is related with the potentials by the condition $|\\lambda(x)|\\leq\\delta a(x)^{\\alpha/p}b(x)^{\\beta/q}$ where $\\delta\\in(0,1)$ and $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09709","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.09709","created_at":"2026-05-18T00:25:28.769386+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09709v2","created_at":"2026-05-18T00:25:28.769386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09709","created_at":"2026-05-18T00:25:28.769386+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWKGUDWFSZ45","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWKGUDWFSZ456W3K","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWKGUDWF","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW","json":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW.json","graph_json":"https://pith.science/api/pith-number/DWKGUDWFSZ456W3K3KL2IGJ6OW/graph.json","events_json":"https://pith.science/api/pith-number/DWKGUDWFSZ456W3K3KL2IGJ6OW/events.json","paper":"https://pith.science/paper/DWKGUDWF"},"agent_actions":{"view_html":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW","download_json":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW.json","view_paper":"https://pith.science/paper/DWKGUDWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09709&json=true","fetch_graph":"https://pith.science/api/pith-number/DWKGUDWFSZ456W3K3KL2IGJ6OW/graph.json","fetch_events":"https://pith.science/api/pith-number/DWKGUDWFSZ456W3K3KL2IGJ6OW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW/action/storage_attestation","attest_author":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW/action/author_attestation","sign_citation":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW/action/citation_signature","submit_replication":"https://pith.science/pith/DWKGUDWFSZ456W3K3KL2IGJ6OW/action/replication_record"}},"created_at":"2026-05-18T00:25:28.769386+00:00","updated_at":"2026-05-18T00:25:28.769386+00:00"}