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Cím:On partial asymptotic stability and instability. II: The method of limiting equation.
Szerző:Hatvani, L.
Forrás:Acta Sci. Math. 46, 143-156 (1983).
Nyelv:English
Absztrakt:The author continues his earlier study of partial stability of the zero solution of $x'=X(x)$ using Lyapunov's direct method [ibid. 46, 143-156 (1983; Zbl 0524.34057)]. The vector x is decomposed as $x=(y,z)$ and the equation is then written as (E) $y'=Y(y,z)$, $z'=Z(y,z)$. In this paper the author treats the case where the right-hand side Y has a uniform limit as the vector z of uncontrolled coordinates tends to infinity in norm. Conditions for the zero solution of (E) to be asymptotically y- stable are given. Extensions to the nonautonomous system (F) $y'=Y(y,z,t)$, $z'=Z(y,z,t)$ are also given.} \RV{P.K.Wong 
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