{"paper":{"title":"On unbounded solutions of ergodic problems in r^m for viscous hamilton-jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"FRDP), Guy Barles (LMPT, Joao Meireles","submitted_at":"2016-09-15T12:29:13Z","abstract_excerpt":"In this article we study ergodic problems in the whole space R m for viscous Hamilton-Jacobi Equations in the case of locally Lips-chitz continuous and coercive right-hand sides. We prove in particular the existence of a critical value $\\lambda$ * for which (i) the ergodic problem has solutions for all $\\lambda$ $\\le$ $\\lambda$ * , (ii) bounded from below solutions exist and are associated to $\\lambda$ * , (iii) such solutions are unique (up to an additive constant). We obtain these properties without additional assumptions in the superquadratic case, while, in the subquadratic one, we assume "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04596","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"}