{"paper":{"title":"Forced periodic solutions for nonresonant parabolic equations on R^N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aleksander Cwiszewski, Renata Lukasiak","submitted_at":"2014-04-01T14:37:17Z","abstract_excerpt":"Criteria for the existence of $T$-periodic solutions of nonautonomous parabolic equation $u_t = \\Delta u + f(t,x,u)$, $x\\in\\mathbb{R}^N$, $t>0$ with asymptotically linear $f$ will be provided. It is expressed in terms of time average function $\\hat f$ of the nonlinear term $f$ and the spectrum of the Laplace operator $\\Delta$ on $\\mathbb{R}^N$. One of them says that if the derivative $\\hat f_\\infty$ of $\\hat f$ at infinity does not interact with the spectrum of $\\Delta$, i.e. $\\mathrm{Ker} (-\\Delta + \\hat f_\\infty)=\\{0\\}$, then the parabolic equation admits a $T$-periodic solution. Another the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0256","kind":"arxiv","version":3},"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"}