非紧半群情形下时滞发展方程周期问题解的存在性  

Existence of Periodic Solutions for Delay Evolution Equations with Noncompact Semigroups

作　　者：李强[1] 魏梅 Li Qiang;Wei Mei(Modern College of Humanities and Sciences, Shanxi Normal University, Linfen 041000, China)

机构地区：[1]山西师范大学现代文理学院,山西临汾041000

出　　处：《宁夏大学学报（自然科学版）》2020年第3期214-219,229,共7页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11261053,11501455)。

摘　　要：在Banach空间X中研究半线性时滞发展方程周期问题:u′(t)+Au(t)=f(t,u(t),ut),t∈R,其中A:D(A)∩X→X为闭线性算子,且-A生成X中的C0-半群T(t)(t≥0),f为连续映射,关于t以ω为周期,ut定义为ut(s)=u(t+s),s∈[-r,0].应用Kuratowski非紧性测度理论及相应的不动点定理,获得了非紧半群情形下周期mild解的存在性.最后,给出了例子说明主要结果的应用.The following semilinear delay evolution equationu′(t)+Au(t)=f(t,u(t),ut),t∈Ris considered in the Banach space X,where A:D(A)∩X→X is a closed linear operator and-A generates a C0-semigroup T(t)(t≥0)in X,f is a continuous function which isω-periodic in t,utis defined by ut(s)=u(t+s),s∈[-r,0].By using tools involving the Kuratowski measure of noncompactness and fixed point theory,some existence results of periodic mild solutions is established without the assumption of compactness on the associated semigroup.In the end,an example is given to illustrate the application of the main results.

关 键 词：发展方程 时滞 Kuratowski非紧性测度 周期mild解 非紧半群 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]