Webproof of Barbalat’s lemma. We suppose that y t) y sequence. ε− ε 2 = ε 2. ε - ε 2 = ε 2. for each n ∈N n ∈ ℕ. By the hypothesis, the improprer Riemann integral ∫∞ 0 y(t)dt ∫ 0 ∞ y ( t) 𝑑 t exists, and thus the left hand side of the inequality converges to 0 as n → ∞ n → ∞, yielding a contradiction . WebBarbalat, I. (1959) Systems d’equations differentiellesd’oscillations nonlineaires. Revue Roumaine des Mathematiques Pureset Appliquees, 4, 267-270. has been cited by the following article: TITLE: Global Dynamics of a Stochastic Two-Prey One-Predator Model with S-Type Distributed Delays and Lévy Noises
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