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arXiv · 1605.09298

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.

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Martin Herdegen, Sebastian Herrmann. 2016-05-30. Minimal Conditions for Implications of Gronwall-Bellman Type. https://arxiv.org/abs/1605.09298

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