Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations

Boundary value problems

Jitao Sun¹  Yueju Cao² 

[1] College of Science, Northwest A&Department of Mathematics, Tongji University, Shanghai, China;F University, Yangling, China

关键词: measure differential equations;    Lebesgue-Stieltjes integral;    \(C_{0}\)-semigroup;    measure of noncompactness;    nonlocal conditions;    34K30;    47H08;    34A37;    34A38;    34G20;    34B10;   

DOI  :  10.1186/s13661-016-0539-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate the existence of mild solutions for abstract semilinear measure driven equations with nonlocal conditions. We first establish some results on Kuratowski measure of noncompactness in the space of regulated functions. Then we obtain some existence results for the abstract measure system by using the measure of noncompactness and a corresponding fixed point theorem. The usual Lipschitz-type assumptions are avoided, and the semigroup related to the linear part of the system is not claimed to be compact, which improves and generalizes some known results in the literature.

【 授权许可】

CC BY