{"paper":{"title":"Exponential stability for nonautonomous functional differential equations with state-dependent delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carmen N\\'u\\~nez, Ismael Maroto, Rafael Obaya","submitted_at":"2017-05-02T10:40:58Z","abstract_excerpt":"The properties of stability of compact set $\\mathcal{K}$ which is positively invariant for a semiflow $(\\Omega\\times W^{1,\\infty}([-r,0],\\mathbb{R}^n),\\Pi,\\mathbb{R}^+)$ determined by a family of nonautonomous FDEs with state-dependent delay taking values in $[0,r]$ are analyzed. The solutions of the variational equation through the orbits of $\\mathcal{K}$ induce linear skew-product semiflows on the bundles $\\mathcal{K}\\times W^{1,\\infty}([-r,0],\\mathbb{R}^n)$ and $\\mathcal{K}\\times C([-r,0],\\mathbb{R}^n)$. The coincidence of the upper-Lyapunov exponents for both semiflows is checked, and it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00898","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"}