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We show that the above $1$-Yamabe equation always has a nontrivial solution $u\\geq0$, $u\\neq0$."},"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":"1709.09867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-28T09:30:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0c3eecbccc99182e3466cf5265090a153e86889133a67686dab55e9557b6cffe","abstract_canon_sha256":"c0a3dfd58048a24907002776074ebcfbf81433190002fce76c37947126edfe6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:06.452061Z","signature_b64":"pbEBwB/UXKv4D3fSdefzzKDsFxm6okEeGbdhHp1s2Mk9w1wRStorKGuR1wGHKczTiKZOXl/2xbRmy6NHlsowBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92d29b59091411372523e781e31ae0aaa85a167a282f59a9dc8e128c8e672918","last_reissued_at":"2026-05-18T00:34:06.451290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:06.451290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $1$-Yamabe equation on graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Huabin Ge, Wenfeng Jiang","submitted_at":"2017-09-28T09:30:31Z","abstract_excerpt":"We study the following $1$-Yamabe equation on a connected finite graph $$\\Delta_1u+g\\mathrm{Sgn}(u)=h|u|^{\\alpha-1}\\mathrm{Sgn}(u),$$ where $\\Delta_1$ is the discrete $1$-Laplacian, $\\alpha>1$ and $g, h>0$ are known. 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