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.

引用

页码：1654 / 1665

页数：12

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