Lipschitz Stability of Nonlinear Systems of Differential Equations
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Author |
Fozi M Dannan - Saber Elaydi |
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Published in |
Journal of mathematical analysis and applications, 113, 562-577, 1986 |
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Abstract |
The main purpose of this paper is to introduce a new notion of stability, which will be called uniform Lipschitz stability, for systems of differential equations. For linear systems, the notions of uniform Lipschitz stability and that of uniform stability are equivalent (Theorem 2.1). However, for nonlinear systems, the two notions are quite distinct (Examples 4.1, 4.2). In fact, uniform Lipschitz stability lies somewhere between uniform stability on one side and the notions of asymptotic stability in variation of Brauer [S] and uniform stability in variation of Brauer and Strauss [7] on the other side. Furthermore, uniform Lipschitz stability neither implies asymptotic stability nor is it implied by it (Example 4.4). |
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