Banach空间中时滞发展方程周期解的存在性与唯一性  

Existence and uniqueness of periodic solutions for delayed evolution equation in Banach spaces

作　　者：李永祥 韦启林 LI Yong-xiang;WEI Qi-lin(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2022年第5期6-11,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12061062,11661071)。

摘　　要：讨论Banach空间X中时滞发展方程u′(t)+Au(t)=f(t,u(t),u(t-τ)),t∈R周期解的存在性与唯一性,其中A:D(A)X X为闭线性算子,-A生成X中的C_(0)-半群T(t)(t≥0),f:R×X×X X连续,f(t,x,y)关于t以ω为周期.应用算子半群理论及不动点定理,获得了方程ω-周期mild解的存在性与唯一性结果,并给出了在时滞偏微分方程中的两个应用实例.The existence and uniqueness of periodic solutions is discussed for the delayed evolution equation in a Banach space X u′(t)+Au(t)=f(t,u(t),u(t-τ)),t∈R,where A:D(A)X X is a closed linear operator,and-A generates a C 0-semigroup T(t)(t≥0)on X,f:R×X×X X is a continuous mapping,f(t,x,y)isω-periodic in t.The existence and uniqueness result ofω-periodic mild solutions are obtained by using the operator semigroups theory and fixed point theorem.Two examples of application in delay partial differential equations are presented.

关 键 词：时滞 发展方程 算子半群 周期mild解 存在性与唯一性 

分 类 号：O175.15[理学—数学]