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∀u, t 0 ≤ u ≤ t g(t) − g(u) ≤ − (λg(s) + C)ds (1) Then

By Quang-cuong Pham

Abstract

We prove a variation of Gronwall’s lemma. The formulation and proof of the classical Gronwall’s lemma can be found in [1]. We prove here a variation of this lemma, which we were not able to find in the literature. Lemma 1 Let g: [0, ∞[ → R be a continuous function, λ> 0 and C ≥ 0. Assume that ∫

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.6128
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