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If $\\Delta_{p}w=\\mbox{div}(|\\nabla w|^{p-2}w)$ stands for the $p-$Laplacian and $\\frac{\\alpha}{p}+\\frac{\\beta}{q}=1,$ we consider $$ \\begin{cases} -\\Delta_pu= \\lambda \\alpha |u|^{\\alpha-2} u|v|^{\\beta} &\\text{ in }\\Omega,\\\\ -\\Delta_q v= \\lambda \\beta |u|^{\\alpha}|v|^{\\beta-2}v &\\text{ in }\\Omega,\\\\ \\end{cases} $$ with mixed boundary conditions $$ u=0, \\qquad |\\nabla v|^{q-2}\\dfrac{\\partial v}{\\partial \\nu }=0, \\qquad \\text{on }\\partial \\Omega. $$ We show that there is a first no"},"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":"1505.07403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-27T17:18:27Z","cross_cats_sorted":[],"title_canon_sha256":"7e24a137fb544a4ee7b7642adf0b58e6e097125ef0918d2cb18bbaff6a66c694","abstract_canon_sha256":"60f7b02d7e003162ca31a443cc5ec472aab215a2ce2a94f61795b4cd746a9064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:10.099402Z","signature_b64":"vd+glrT4BHIwYtJiVMcldXvtfUVLROPvgxHiF/i22sy6rSPu2UTpljYKll+s/neMTFBJFsdrm9+tj1i9GKMbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e960d78bfaa897750bae857390f013bfe04d95b01ae1677550b0b0402dd4fb","last_reissued_at":"2026-05-18T01:17:10.098577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:10.098577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first nontrivial eigenvalue for a system of $p-$Laplacians with Neumann and Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2015-05-27T17:18:27Z","abstract_excerpt":"We deal with the first eigenvalue for a system of two $p-$Laplacians with Dirichlet and Neumann boundary conditions. If $\\Delta_{p}w=\\mbox{div}(|\\nabla w|^{p-2}w)$ stands for the $p-$Laplacian and $\\frac{\\alpha}{p}+\\frac{\\beta}{q}=1,$ we consider $$ \\begin{cases} -\\Delta_pu= \\lambda \\alpha |u|^{\\alpha-2} u|v|^{\\beta} &\\text{ in }\\Omega,\\\\ -\\Delta_q v= \\lambda \\beta |u|^{\\alpha}|v|^{\\beta-2}v &\\text{ in }\\Omega,\\\\ \\end{cases} $$ with mixed boundary conditions $$ u=0, \\qquad |\\nabla v|^{q-2}\\dfrac{\\partial v}{\\partial \\nu }=0, \\qquad \\text{on }\\partial \\Omega. $$ We show that there is a first no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07403","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":"1505.07403","created_at":"2026-05-18T01:17:10.098698+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.07403v2","created_at":"2026-05-18T01:17:10.098698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07403","created_at":"2026-05-18T01:17:10.098698+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHUWBV4L7KUJ","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHUWBV4L7KUJO5IL","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHUWBV4L","created_at":"2026-05-18T12:29:47.479230+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/WHUWBV4L7KUJO5ILV2CXHEHQCO","json":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO.json","graph_json":"https://pith.science/api/pith-number/WHUWBV4L7KUJO5ILV2CXHEHQCO/graph.json","events_json":"https://pith.science/api/pith-number/WHUWBV4L7KUJO5ILV2CXHEHQCO/events.json","paper":"https://pith.science/paper/WHUWBV4L"},"agent_actions":{"view_html":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO","download_json":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO.json","view_paper":"https://pith.science/paper/WHUWBV4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.07403&json=true","fetch_graph":"https://pith.science/api/pith-number/WHUWBV4L7KUJO5ILV2CXHEHQCO/graph.json","fetch_events":"https://pith.science/api/pith-number/WHUWBV4L7KUJO5ILV2CXHEHQCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO/action/storage_attestation","attest_author":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO/action/author_attestation","sign_citation":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO/action/citation_signature","submit_replication":"https://pith.science/pith/WHUWBV4L7KUJO5ILV2CXHEHQCO/action/replication_record"}},"created_at":"2026-05-18T01:17:10.098698+00:00","updated_at":"2026-05-18T01:17:10.098698+00:00"}