{"paper":{"title":"On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Alberto Lastra, St\\'ephane Malek","submitted_at":"2013-07-17T13:43:13Z","abstract_excerpt":"We study a family of singularly perturbed $q-$difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter $\\epsilon$. Moreover, we achieve the existence of a common formal power series in $\\epsilon$ which represents each actual solution, and establish $q-$Gevrey estimates involved in this representation. The proof of the main result rests on a new version of the so-called Malgrange-Sibuya Theorem regarding $q-$Gevrey asymptotics. A particular Dirichlet like series is studied on the way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4627","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"}