Banach空间半线性发展方程周期解的存在性结果及应用  

Existence Results of Periodic Solutions for Semilinear Evolution Equation in Banach Spaces and Applications

作　　者：李永祥 韦启林 Li Yongxiang;Wei Qilin(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学物理学报（A辑）》2023年第3期702-712,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(12061062,11661071)~。

摘　　要：该文讨论了Banach空间X中抽象半线性发展方程u′(t)+Au(t)=f(t,u(t)),t∈R周期解的存在性,其中A:D(A)⊂X→X为闭线性算子,−A生成X上的C_(0)-半群,f:R×X→X连续,f(t,x)关于t以ω为周期.我们应用算子半群理论、非紧性测度的估计技巧与不动点定理,获得了该方程ω-周期mild解的存在性结果,并给出了在抛物型偏微分方程与弱阻尼波方程中应用的例子.In this paper,we deal with the existence of periodic solutions for the semilinear evolution equation in a Banach space X,u′(t)+Au(t)=f(t,u(t)),t∈R,where A:D(A)⊂X→X is a closed linear operator and−A generates a C_(0)-semigroup X,f:R×X→X is a continuous mapping and f(t,x)isω-periodic in t.Existence results ofω-periodic mild solutions are obtained by using operator semigroup theory,estimation technique of noncompact measure and fixed point theorem.Examples of applications in parabolic partial differential equations and weakly damped wave equations are present.

关 键 词：半线性发展方程 算子半群 非紧性测度 周期mild解 存在性 

分 类 号：O175.15[理学—数学]