非自治中立型无穷时滞泛函微分方程的加权伪概自守解  

Weighted pseudo almost automorphic solutions for non-autonomous neutral functional differential equations with infinite delay

作　　者：张蕊[1] 常永奎[1] N'GUEREKATA Gaston Mandata 

机构地区：[1]兰州交通大学数学系,兰州730070 [2]Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

出　　处：《中国科学：数学》2013年第3期273-292,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10901075);教育部新世纪优秀人才支持计划(批准号:NCET-10-0022);教育部科学技术重点项目(批准号:210226);甘肃省自然科学基金(批准号:1107RJZA091)资助项目

摘　　要：首先引入h型Stepanov加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念,接着建立了其函数空间的完备性以及相应组合定理,最后证明了一类非自治无穷时滞偏中立型泛函微分方程在Sp-加权伪概自守系数下加权伪概自守解的存在唯一性.We first introduce the notion of Stepanov-like weighted pseudo almost automorphic functions of class h and the notion of Stepanov-like weighted pseudo almost automorphic functions of class ∞, and then establish some basic results not only on the completeness of the space that consists of the SP-weighted pseudo almost automorphic functions of class h and class ∞ but also on the compositions of such functions. Finally, we apply the abstract results to prove the existence and uniqueness of weighted pseudo almost automorphic solutions with SP-weighted pseudo almost automorphic coefficients to a non-autonomous first-order abstract partial neutral functional differential equation with infinite delay.

关 键 词：Stepanov加权伪概自守函数 无穷时滞 泛函微分方程 

分 类 号：O241.8[理学—计算数学]