扇形算子情形下时滞发展方程周期解的存在性
Existence of Periodic Solutions for Delayed Evolution Equation with Sector Operator
摘要: 本文讨论了Banach 空间X中时滞发展方程周期解的存在性，其中A:D(A)⊂X→X为扇形算子，−A生成X中指数稳定的解析半群T(t)(t≥0),f:ℝ×Xn+1→X连续，关于t以ω为周期，τ1, •••,τn > 0。我们应用不动点定理，获得了方程ω-周期mild 解的存在性结果。
Abstract: This paper deals with the existence of periodic solutions for delayed evolution equation in a Banach space X, where A:D(A)⊂X→X is a sector operator and −A generates a exponential stability analytic semigroup T(t)(t≥0),f:ℝ×Xn+1→X is a continuous function mapping and it is ω-periodic in τ1, •••,τn > 0. Existence results of ω-periodic mild solutions are obtained by using the fixed point theorem.
文章引用：韦启林. 扇形算子情形下时滞发展方程周期解的存在性[J]. 理论数学, 2022, 12(4): 653-664. https://doi.org/10.12677/PM.2022.124075

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