{"paper":{"title":"On the asymptotic behavior of the solutions of semilinear nonautonomous equations","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.CA","authors_text":"Ciprian Preda, Gaston M. N'gu\\'er\\'ekata, Nguyen Van Minh","submitted_at":"2012-11-21T20:03:20Z","abstract_excerpt":"We consider nonautonomous semilinear evolution equations of the form\n\\label{semilineq} \\frac{dx}{dt}= A(t)x+f(t,x).\nHere $A(t)$ is a (possibly unbounded) linear operator acting on a real or complex Banach space $\\X$ and $f: \\R\\times\\X\\to\\X$ is a (possibly nonlinear) continuous function. We assume that the linear equation \\eqref{lineq} is well-posed (i.e. there exists a continuous linear evolution family \\Uts such that for every $s\\in\\R_+$ and $x\\in D(A(s))$, the function $x(t) = U(t, s) x$ is the uniquely determined solution of equation \\eqref{lineq} satisfying $x(s) = x$). Then we can conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5126","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"}