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About: Bihari–LaSalle inequality     Goto   Sponge   NotDistinct   Permalink

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The Bihari–LaSalle inequality, was proved by the American mathematicianJoseph P. LaSalle (1916–1983) in 1949 and by the Hungarian mathematicianImre Bihari (1915–1998) in 1956. It is the following nonlinear generalization of Grönwall's lemma. Let u and ƒ be non-negative continuous functions defined on the half-infinite ray [0, ∞), and let w be a continuous non-decreasing function defined on [0, ∞) and w(u) > 0 on (0, ∞). If u satisfies the following integral inequality, where α is a non-negative constant, then where the function G is defined by