{"paper":{"title":"Periodic solutions for completely resonant nonlinear wave equations","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Guido Gentile, Michela Procesi, Vieri Mastropietro","submitted_at":"2004-02-16T18:08:36Z","abstract_excerpt":"We consider the nonlinear string equation with Dirichlet boundary conditions $u_{xx}-u_{tt}=\\phi(u)$, with $\\phi(u)=\\Phi u^{3} + O(u^{5})$ odd and analytic, $\\Phi\\neq0$, and we construct small amplitude periodic solutions with frequency $\\o$ for a large Lebesgue measure set of $\\o$ close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and nonresonant Fourier co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402262","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"}