{"paper":{"title":"Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Douglas D. Novaes, Jaume Llibre, Murilo R. C\\^andido","submitted_at":"2016-11-15T12:36:35Z","abstract_excerpt":"In this work we first provide sufficient conditions to assure the persistence of some zeros of functions having the form $$g(z,\\varepsilon)=g_0(z)+\\sum_{i=1}^k \\varepsilon^i g_i(z)+\\mathcal{O}(\\varepsilon^{k+1}),$$ for $|\\varepsilon|\\neq0$ sufficiently small. Here $g_i:\\mathcal{D}\\rightarrow\\mathbb{R}^n$, for $i=0,1,\\ldots,k$, are smooth functions being $\\mathcal{D}\\subset \\mathbb{R}^n$ an open bounded set. Then we use this result to compute the bifurcation functions which controls the periodic solutions of the following $T$-periodic smooth differential system $$ x'=F_0(t,x)+\\sum_{i=1}^k \\vare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04807","kind":"arxiv","version":2},"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"}