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We prove the existence of a nonnegative ground state $(u_1^*,\\ldots,u_d^*)$ with $u_i^*$ radially decreasing. Moreover we show that, for $1<q<2$, such ground states are"},"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":"1504.04655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-17T22:40:25Z","cross_cats_sorted":[],"title_canon_sha256":"3da61c0b290997b397486f111b564835e1b71c287a827efb9d61655472bf24ec","abstract_canon_sha256":"b97435ba8a8d3a5e37e2613315337ebc7f3cddf21504bfb5df370e6e3d80bacd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:30.781109Z","signature_b64":"woNmP6/qJUu33n4Y7N9eciduvs2hpUCojs2Wr+85O15+EkO/47jLhM3ehQM9YF6Ilh+F10YiQ0uXH9tTmF27CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc087693844eb15aca462cf3a947b8f2a13afffa3377f7ce34427f38003d62b8","last_reissued_at":"2026-05-18T02:18:30.780555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:30.780555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground States for a nonlinear Schr\\\"odinger system with sublinear coupling terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira, Hugo Tavares","submitted_at":"2015-04-17T22:40:25Z","abstract_excerpt":"We study the existence of ground states for the coupled Schr\\\"odinger system\n  \\begin{equation} \\left\\{\\begin{array}{lll} \\displaystyle -\\Delta u_i+\\lambda_i u_i= \\mu_i |u_i|^{2q-2}u_i+\\sum_{j\\neq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i \\\\ u_i\\in H^1(\\mathbb{R}^n), \\quad i=1,\\ldots, d, \\end{array}\\right. \\end{equation} $n\\geq 1$, for $\\lambda_i,\\mu_i >0$, $b_{ij}=b_{ji}>0$ (the so-called \"symmetric attractive case\") and $1<q<n/(n-2)^+$. We prove the existence of a nonnegative ground state $(u_1^*,\\ldots,u_d^*)$ with $u_i^*$ radially decreasing. Moreover we show that, for $1<q<2$, such ground states are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04655","kind":"arxiv","version":1},"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":"1504.04655","created_at":"2026-05-18T02:18:30.780638+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04655v1","created_at":"2026-05-18T02:18:30.780638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04655","created_at":"2026-05-18T02:18:30.780638+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QEHNE4EJ2YV","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QEHNE4EJ2YVVSSG","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QEHNE4E","created_at":"2026-05-18T12:29:10.953037+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/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K","json":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K.json","graph_json":"https://pith.science/api/pith-number/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/graph.json","events_json":"https://pith.science/api/pith-number/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/events.json","paper":"https://pith.science/paper/7QEHNE4E"},"agent_actions":{"view_html":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K","download_json":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K.json","view_paper":"https://pith.science/paper/7QEHNE4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04655&json=true","fetch_graph":"https://pith.science/api/pith-number/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/graph.json","fetch_events":"https://pith.science/api/pith-number/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/action/storage_attestation","attest_author":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/action/author_attestation","sign_citation":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/action/citation_signature","submit_replication":"https://pith.science/pith/7QEHNE4EJ2YVVSSGFTZ2SR5Y6K/action/replication_record"}},"created_at":"2026-05-18T02:18:30.780638+00:00","updated_at":"2026-05-18T02:18:30.780638+00:00"}