Una aplicación del teorema de liberalización de hartman
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→0 f(t, U) = 0 and lim U→0 Df(t, U) = 0 u...
- Autores:
-
Naulin, Raúl
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1991
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43398
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43398
http://bdigital.unal.edu.co/33496/
- Palabra clave:
- Ordinary differential equation
matrix constant eigenvalues
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | 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→0 f(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 and gt; 0, there exists δ (μ) and gt; 0 such that for solutions U1, U2 with initial conditions ξ1, ξ 2, ξ 1 "# ξ2, |ξ1| and lt; δ we havem limt→∞|U1 (t) – U2 (t)| eμt = ∞. |
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