抽象半线性发展方程正周期解的存在唯一性  

EXISTENCE AND UNIQUENESS OF POSITIVE PERIODIC SOLUTIONS FOR ABSTRACT SEMILINEAR EVOLUTION EQUATIONS

作　　者：李永祥[1] 

机构地区：[1]西北师范大学数学系,兰州730070

出　　处：《系统科学与数学》2005年第6期720-728,共9页Journal of Systems Science and Mathematical Sciences

基　　金：甘肃省自然科学基金(ZS031-A25-003-Z)NWNU-KJCXGC-212基金资助课题.

摘　　要：讨论有序Banach空间E中半线性发展方程 u′(t)+Au(t)=f(t,u(t)),t∈R, ω-周期解的存在性,其中A为E中正C0-半群的生成元,f:R×E→E连续,关于t 以ω为周期．我们对相应的线性发展方程建立了周期解的存在唯一性,并对周期解算子的谱半径作了精确估计．借助于这个估计,我们用单调迭代方法获得了半线性发展方程正ω-周期解的存在唯一性．This paper discusses the existence of w-periodic solutions for semilinear evolution equation u′（t）＋Au（t）=f（t,u（t））,t∈R in an ordered Banach space E, where A is the infinitesimal generator of a positive Co -semigroup, and f：R×E→E E is a continuous mapping which is w-periodic in t. The existence and uniqueness results of periodic solutions for the associated linear evolution equation is established, and the spectral radius of periodic resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness results of positive periodic solutions are obtained by using monotone iterative technique.

关 键 词：抽象发展方程 正C0-半群 周期解 谱半径 存在唯一性 

分 类 号：O177.91[理学—数学]