Una aplicación del teorema de liberalización de Hartman

Autores: Raúl Naulin
Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 25, Nº. 1-4, 1991, págs. 11-16
Idioma: español
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Resumen
- In this note we consider the ordinary differential equation U' = AU +f(t, U), where A is a real, constant, n x n matrix with eigenvalues satisfying Reλ = 0. We assume that the solution U = 0 of the system U' =A U is stable. f is a C1 function, lim U→0f(t, U) = 0 and lim U→0 Df(t, U) = 0 uniformly in t (Df is derivate of f with respect to U). We prove that for any μ > 0, there exists δ (μ) > 0 such that for solutions U1, U2 with initial conditions ξ1, ξ 2, ξ 1 "# ξ2, |ξ1| < δ we havem limt→∞|U1 (t) – U2 (t)| eμt = ∞.