Measure of Noncompactness and Semilinear Nonlocal Functional Differential Equations in Banach Spaces  

作　　者：Qi Xiang DONG Gang LI 

机构地区：[1]School of Mathematical Sciences, Yangzhou University

出　　处：《Acta Mathematica Sinica,English Series》2015年第1期140-150,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11271316 and 11201410);Natural Science Foundation of Jiangsu Province(Grant No.BK2012260)

摘　　要：This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonloeal conditions in Banach spaces. The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces. The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups Of linear operators.This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonloeal conditions in Banach spaces. The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces. The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups Of linear operators.

关 键 词：Measure of noncompactness EQUICONTINUITY differential equation nonlocal condition C0-SEMIGROUP mild solution 

分 类 号：O177.2[理学—数学] O175[理学—基础数学]