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Under mild structural hypotheses on the coefficients and on the existence of a stable moving equilibrium branch $E(x)$, we prove a new \\emph{Asymptotic Plateau Theorem} establishing that the solution issued from $y(x_0)=0$ is globally defined, strictly monotone, trapped between zero and $E(x)$, and converges to a finite positi"},"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":true},"canonical_record":{"source":{"id":"2605.02831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-04T17:07:25Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"ffcffab8ef20bf71169cf7c05ab94ca5bf34129f99c475827f8f6918877e0f09","abstract_canon_sha256":"9eda40382fb61959ad925d88ba89ae8a9358dc74e051bf876d273e16e95d1174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:33.781847Z","signature_b64":"dmzG78LCZE4l/GQ/fvIoO2h5FRqrS2D8lBMfN/CM0ild+KYxumpHCt5jAotNwiMFMYzkn4RL+ReugKa4hvgFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14d70450424d7092616181879fb282f0a8ff2261aba6388ad068609646b8cd58","last_reissued_at":"2026-05-20T00:04:33.781009Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:33.781009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Plateaus for Generalized Abel Equations with Financial Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Generalized Abel differential equations with any polynomial degree n greater than or equal to 1 possess regular solutions that exhibit sharp growth rates and exact asymptotic plateaus on bounded and unbounded domains.","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Dragos-Patru Covei","submitted_at":"2026-05-04T17:07:25Z","abstract_excerpt":"We develop a unified analytical and computational framework for the generalized Abel ordinary differential equation $y^{\\prime }(x)=a_n(x)\\bigl(% y^n+\\lambda_{n-1}(x)y^{n-1}+\\dots+\\lambda_0(x)\\bigr)$ of arbitrary degree $% n\\ge1$ on the unbounded interval $[x_0,\\infty)$. Under mild structural hypotheses on the coefficients and on the existence of a stable moving equilibrium branch $E(x)$, we prove a new \\emph{Asymptotic Plateau Theorem} establishing that the solution issued from $y(x_0)=0$ is globally defined, strictly monotone, trapped between zero and $E(x)$, and converges to a finite positi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present a comprehensive investigation into a generalized class of Abel ordinary differential equations (ODEs), extending the classical cubic form to arbitrary polynomial nonlinearities of degree n ≥ 1. 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