Minimal conditions for implications of Gronwall-Bellman type

被引：2
|
作者：
Herdegen, Martin [1 ]
Herrmann, Sebastian [2 ]
机构：
[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England
[2] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 446卷 / 02期
基金：
瑞士国家科学基金会;
关键词：
Gronwall-Bellman inequalities; Integral inequalities; Semi-finite measures; STIELTJES INTEGRAL-INEQUALITIES; MEASURE-SPACES; EQUATIONS;
D O I：
10.1016/j.jmaa.2016.09.054
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Gronwall-Bellman type inequalities entail the following implication: if a sufficiently integrable function satisfies a certain homogeneous linear integral inequality, then it is nonpositive. We present a minimal (necessary and sufficient) condition on the Borel measure underlying the integrals for this implication to hold. The condition is also a necessary prerequisite for any nontrivial bound on solutions to inhomogeneous linear integral inequalities of Gronwall-Bellman type. (C) 2016 Elsevier Inc. All rights reserved.
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页码：1654 / 1665
页数：12
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