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Cím:On the asymptotic stability by Lyapunov function with semidefinite derivative.
Szerző:Hatvani, L.
Forrás:Trends in theory and practice of nonlinear differential equations, Proc. int. Conf., Arlington/Tex. 1982, Lect. Notes Pure Appl. Math. 90, 247-253 (1984).
Absztrakt:[For the entire collection see Zbl 0519.00009.] \par Sufficient conditions for the asymptotic stability and partial asymptotic stability of the zero solution of a differential system are given by the use of Lyapunov's direct method. In nonautonomous case the derivative of the Lyapunov function is assumed to be estimated: \.V(t,x)$\le - \phi(t)U(x)$, where $\phi$ (t) is integrally positive or weakly integrally positive, U(x) positive semidefinite. \par By the help of the method of limiting equation a sufficient condition for the partial asymptotic stability of the zero solution of an autonomous system is found without requiring boundedness of the uncontrolled coordinates. The results are applied to the study of stability properties of equilibria in mechanical systems being under the action of dissipative forces. 
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