{"paper":{"title":"Positive periodic solutions for abstract evolution equations with delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Mei Wei, Qiang Li, Yongxiang Li","submitted_at":"2018-01-02T08:09:37Z","abstract_excerpt":"In this paper, we discuss the existence and asymptotic stability of the positive periodic mild solutions for the abstract evolution equation with delay in an ordered Banach space $E$, $$u'(t)+Au(t)=F(t,u(t),u(t-\\tau)),\\ \\ \\ \\ t\\in\\R,$$ where $A:D(A)\\subset E\\rightarrow E$ is a closed linear operator and $-A$ generates a positive $C_{0}$-semigroup $T(t)(t\\geq0)$, $F:\\R\\times E\\times E\\rightarrow E$ is a continuous mapping which is $\\omega$-periodic in $t$.\n  Under order conditions on the nonlinearity $F$ concerning the growth exponent of the semigroup $T(t)(t\\geq0)$ or the first eigenvalue of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00573","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"}