On generic asymptotic stability of differential equations in Banach space
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- by F. S. De Blasi and J. Myjak
- Proc. Amer. Math. Soc. 65 (1977), 47-51
- DOI: https://doi.org/10.1090/S0002-9939-1977-0447730-0
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Abstract:
The asymptotic stability of the zero solution of the differential equation $( \ast )\;x’ = Ax + f(x)$ is studied, when the pertubation f is in a given complete metric space $\mathfrak {M}$. It is known that the zero solution of $( \ast )$ is asymptotically stable whenever f is in a certain proper subset $\mathfrak {N} \subset \mathfrak {M}$. It is shown that, while $\mathfrak {N}$ is of Baire first category in $\mathfrak {M}$, on the contrary the set ${\mathfrak {M}_0}$ of all those f for which the zero solution of $( \ast )$ is asymptotically stable is a proper residual subset of $\mathfrak {M}$.References
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Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 47-51
- MSC: Primary 34G05; Secondary 58F10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0447730-0
- MathSciNet review: 0447730