Maximal Regularity of Second Order Delay Equations in Banach Spaces  

作　　者：Shang Quan BU 

机构地区：[1]Department of Mathematical Science, Tsinghua University, Beijing 100084, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第1期21-28,共8页数学学报（英文版）

基　　金：supported by the NSF of China (No. 10571099);Specialized Research Fund for the Doctoral Program of Higher Education;the Tsinghua Basic Research Foundation (JCpy2005056)

摘　　要：Using known Ca-multiplier result, we give necessary and sufficient conditions for the second order delay equations：u″（t）=Au（t）＋Fut＋Gu′＋f（t）,t∈Rto have maximal regularity in HSlder continuous function spaces C^α （R, X）, where X is a Banach space, A is a closed operator in X, F, G ∈L（C（[-r, 0], X）, X） are delay operators for some fixed r 〉 0.Using known Ca-multiplier result, we give necessary and sufficient conditions for the second order delay equations：u″（t）=Au（t）＋Fut＋Gu′＋f（t）,t∈Rto have maximal regularity in HSlder continuous function spaces C^α （R, X）, where X is a Banach space, A is a closed operator in X, F, G ∈L（C（[-r, 0], X）, X） are delay operators for some fixed r 〉 0.

关 键 词：maximal regularity delay equations Hoelder continuous functions C^α-multiplier 

分 类 号：O175[理学—数学]