Boundedness and asymptotic stability in the large of solutions of an ordinary differential system \(y'= f(t,y,y')\) (Q1201973)
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scientific article; zbMATH DE number 98946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundedness and asymptotic stability in the large of solutions of an ordinary differential system \(y'= f(t,y,y')\) |
scientific article; zbMATH DE number 98946 |
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Boundedness and asymptotic stability in the large of solutions of an ordinary differential system \(y'= f(t,y,y')\) (English)
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19 January 1993
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The authors continue the study of stability properties of a ``nonstandard'' ordinary differential system started in [ibid. 4, No. 3, 211-224 (1991; Zbl 0736.34052)]. The system under consideration is of the form \(y'=f(t,y,y')\); a crucial assumption is that \(f(t,y,z)\) satisfies a Lipschitz condition with respect to \(z\) with a Lipschitz constant \(k_ z<1\). In the context of Lyapunov's direct method the authors obtain sufficient conditions for several types of ultimate boundedness and global asymptotic stability.
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nonstandard ordinary differential system
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Lipschitz condition
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Lyapunov's direct method
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ultimate boundedness
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global asymptotic stability
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