{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NH25FQOMGHFZ4CXSV5G2AX5TPX","short_pith_number":"pith:NH25FQOM","schema_version":"1.0","canonical_sha256":"69f5d2c1cc31cb9e0af2af4da05fb37dce0249ae4ca6694d24da5f226b712dee","source":{"kind":"arxiv","id":"1403.7106","version":1},"attestation_state":"computed","paper":{"title":"Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Minne, Martin H. Str\\\"omqvist","submitted_at":"2014-03-27T15:56:18Z","abstract_excerpt":"We introduce so called balanced quasi-monotone systems. These are systems $F(x,r,p,X)=(F_1(x,r,p,X),\\ldots,F_m(x,r,p,X))$, where $x$ belongs to a domain $\\Omega$, $r=u(x)\\in\\mathbb{R}^m$, $p=Du(x)$ and $X=D^2u(x)$, that can be arranged into two categories that are mutually competitive but internally cooperative. More precisely, for all $i\\neq j$ in the set $\\{1,2,\\ldots,m\\}$, $F_j$ is monotone non-decreasing (non-increasing) in $r_i$ if and only if $F_i$ is monotone non-decreasing (non-increasing) in $r_j$ and $F_j$ is a monotone function in $r_i$. We prove the existence and uniqueness of visc"},"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":"1403.7106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-27T15:56:18Z","cross_cats_sorted":[],"title_canon_sha256":"d5a9bb721694316f326fc5ecc4edfacf483d51e50870f4a2d947960b10b7d098","abstract_canon_sha256":"d3f2c3e39eceb8a11c35ce354250688a3f5ad42e7860c05fa415e8d6edca8a0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:26.501525Z","signature_b64":"uojz5vrLKqXRij1hHAcDD3ExJ+ii12Mc2FjU+Z/A8h/BRBv0S5wmahUedgjYQoZri2R1gbrCFhd2FDKmZQnKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69f5d2c1cc31cb9e0af2af4da05fb37dce0249ae4ca6694d24da5f226b712dee","last_reissued_at":"2026-05-18T02:55:26.501062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:26.501062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Minne, Martin H. Str\\\"omqvist","submitted_at":"2014-03-27T15:56:18Z","abstract_excerpt":"We introduce so called balanced quasi-monotone systems. These are systems $F(x,r,p,X)=(F_1(x,r,p,X),\\ldots,F_m(x,r,p,X))$, where $x$ belongs to a domain $\\Omega$, $r=u(x)\\in\\mathbb{R}^m$, $p=Du(x)$ and $X=D^2u(x)$, that can be arranged into two categories that are mutually competitive but internally cooperative. More precisely, for all $i\\neq j$ in the set $\\{1,2,\\ldots,m\\}$, $F_j$ is monotone non-decreasing (non-increasing) in $r_i$ if and only if $F_i$ is monotone non-decreasing (non-increasing) in $r_j$ and $F_j$ is a monotone function in $r_i$. 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