{"paper":{"title":"Young Differential Equations with Power Type Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Jorge A. Le\\'on, Samy Tindel","submitted_at":"2016-06-07T18:44:05Z","abstract_excerpt":"In this note we give several methods to construct nontrivial solutions to the equation $dy_{t}=\\sigma(y_{t}) \\, dx_{t}$, where $x$ is a $\\gamma$-H\\\"older $R^{d}$-valued signal with $\\gamma\\in(1/2,1)$ and $\\sigma$ is a function behaving like a power function $|\\xi|^{\\kappa}$, with $\\kappa\\in(0,1)$. In this situation, classical Young integration techniques allow to get existence and uniqueness results whenever $\\gamma(\\kappa+1)>1$, while we focus on cases where $\\gamma(\\kappa+1)\\le 1$. Our analysis then relies on some extensions of Young's integral allowing to cover the situation at hand."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02258","kind":"arxiv","version":1},"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"}