A generalization of Barbashin-Krasovski theorem |
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| Authors: | Liangping Jiang |
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| Affiliation: | a Department of Mathematics, College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, People's Republic of China
b Center of Mathematics Sciences at Zhejiang University, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China |
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| Abstract: | The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that  for some c∈K. In this paper we prove that if f(t,x) is bounded,  is uniformly continuous and bounded, then the condition that  can be weakened and replaced by  and  contains no complete trajectory of  , t∈[−T,T], where  ,  uniformly for (t,x)∈[−T,T]×BH. |
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| Keywords: | Asymptotic stability Lyapunov's direct method Barbashin-Krasovski theorem |
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