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Minimal conditions for implications of Gronwall-Bellman
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Herdegen, Martin and Herrmann, Sebastian (2017) Minimal conditions for implications of Gronwall-Bellman. Journal of Mathematical Analysis and Applications, 446 (2). pp. 1654-1665. ISSN 0022-247X.
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Official URL: http://dx.doi.org/10.1016/j.jmaa.2016.09.054
Abstract
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.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Library of Congress Subject Headings (LCSH): | Gronwall inequalities, Integral inequalities | ||||||||||
Journal or Publication Title: | Journal of Mathematical Analysis and Applications | ||||||||||
Publisher: | Academic Press | ||||||||||
ISSN: | 0022-247X | ||||||||||
Official Date: | 14 February 2017 | ||||||||||
Dates: |
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Volume: | 446 | ||||||||||
Number: | 2 | ||||||||||
Page Range: | pp. 1654-1665 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 7 December 2016 | ||||||||||
Date of first compliant Open Access: | 29 September 2017 | ||||||||||
Funder: | Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung [Swiss National Science Foundation] (SNSF), Swiss Finance Institute | ||||||||||
Grant number: | SNF105218_150101 (SNSF) | ||||||||||
Open Access Version: |
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