Minimal conditions for implications of Gronwall–Bellman type

Martin Herdegen, Sebastian Herrmann

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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.
Original languageUndefined
JournalJournal of Mathematical Analysis and Applications
Early online date29 Sept 2016
DOIs
Publication statusPublished - Feb 2017

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