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Here we prove the existence of a critical curve $\\Gamma$ whic"},"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":"1901.02728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-09T13:30:48Z","cross_cats_sorted":[],"title_canon_sha256":"7e0ce442e9caae5eea74103235648672d68efefd3d9f5c4464792bccd5121ad7","abstract_canon_sha256":"3dbd827fd2e8f90c874d711bf5f6bb9e4627e37398d563bc73f79884a09e9d52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.620610Z","signature_b64":"aS9s7Ecezms526fSl+xnrxRQw1KmocknUp+n6P1oPaEaF24b+Jbfm7sCji6wKTStj77jwSE2DqLKiLgW7dTkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfdbac4ea4289477b991b05e0df1c5d264033603f43bd904c12cc266807dca6c","last_reissued_at":"2026-05-17T23:56:39.619892Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.619892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Lane-Emden systems with singular nonlinearities and applications to MEMS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Rodrigo Clemente","submitted_at":"2019-01-09T13:30:48Z","abstract_excerpt":"In this paper we analyse the Lane-Emden system \\begin{equation} \\left\\{ \\begin{alignedat}{3} -\\Delta u = & \\, \\frac{\\lambda f(x)}{(1-v)^2} & \\quad \\text{in} & \\quad\\Omega\\\\ -\\Delta v = & \\, \\frac{\\mu g(x)}{(1-u)^2} & \\quad \\text{in} & \\quad\\Omega\\\\ 0\\leq u &, v < 1 & \\quad \\text{in} & \\quad \\Omega\\\\ u = v & = \\, 0 & \\text{on} & \\quad \\partial\\Omega\\\\ \\end{alignedat} \\right.\\tag{$S_{\\lambda, \\mu}$} \\end{equation} where $\\lambda$ and $\\mu$ are positive parameters and $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^N$ $( N \\geq 1)$. 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