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

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• 作者：Yueju Cao ; Jitao Sun
• 关键词：34K30 ; 47H08 ; 34A37 ; 34A38 ; 34G20 ; 34B10 ; measure differential equations ; Lebesgue ; Stieltjes integral ; C 0 $C_{0}$ ; semigroup ; measure of noncompactness ; nonlocal conditions
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,729 KB
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• 作者单位：Yueju Cao (1) (2)
  Jitao Sun (1)
  
  1. Department of Mathematics, Tongji University, Shanghai, 200092, China
  2. College of Science, Northwest A&F University, Yangling, Shanxi, 712100, China
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

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. Keywords measure differential equations Lebesgue-Stieltjes integral \(C_{0}\)-semigroup measure of noncompactness nonlocal conditions