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Some General Theorems on Uniform Boundedness for Functional Differential Equations

Author
Wang, Tingxiu

Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1460
Abstract
Consider the functional differential equation with bounded delayX′ = F(t,Xt), X ∈ Rn. We discuss uniform boundedness and uniform ultimate boundedness by Liapunov’s second method with conditions such as: (i) W1(|X(t)|) ≤ V(t, Xt) ≤ W2(|X(t)| +  (ii) V(t, φ) ≤ W3(‖φ‖); (iii) V′(1) (t, Xt) ≤ where m(φ) = min−h≤s≤0|φ(s)|. The theorem discussed in this paper generalizes some results on uniform boundedness and uniform ultimate boundedness for functional differential equations with bounded delay. Some examples are also discussed in this paper.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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