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

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。

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.