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A new criterion for the global stability of equilibria is derived for nonlinear autonomous ordinary differential equations in any finite dimension based on recent developments in higher-dimensional generalizations of the criteria of Bendixson and Dulac for planar systems and on a local version of the C¹ closing lemma of Pugh. The classical result of Lyapunov is obtained as a special case.
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Li et al. (1996) studied this question.
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