Banach空间中双扰动无穷时滞微分方程  

DOUBLE PERTURBED DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN BANACH SPACES

作　　者：毋光先[1,2] 董琪翔[1] 李刚[1] 

机构地区：[1]扬州大学数学科学学院,扬州225117 [2]焦作师范高等专科学校数学系,焦作454001

出　　处：《南京大学学报（数学半年刊）》2010年第1期124-133,共10页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：国家自然科学基金资助项目(10971182);江苏省高校自然科学基金资助项目(09KJB110010)

摘　　要：利用Hausdorff非紧性测度、线性算子半群和不动点理论,给出了当相关半群非紧等较弱的条件下,实Banach空间中一类双扰动的无穷时滞微分方程适度解的存在性.所用的方法可对相关半群是紧半群、扰动函数都是Lipschitz函数或者扰动函数为紧映射等情况进行统一处理.This paper is concerned with the existence of mild solutions to a class of double perturbed differential equations with infinite delay in Banach spaces by using the theory of Hausdorff＇s measure of non-compactness,semi-groups of linear operators and fixed point theorem under some relatively weak conditions,such as the relative semi-group is not compact.In the technical framework developed in this work,several cases can be dealed with simultaneously,such as the relative semigroup is compact,the perturbation functions are compact or the perturbation functions satisfy Lipschitz-type condition.

关 键 词：无穷时滞微分方程 适度解 Hausdorff非紧性测度 线性算子半群 

分 类 号：O175.15[理学—数学]