Asymptotic equilibrium, periodic solutions, and Lyapunov's direct method (Q2703978)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic equilibrium, periodic solutions, and Lyapunov's direct method |
scientific article |
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3 February 2002
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differential equation
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asymptotic equilibrium
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periodic solutions
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Lyapunov's direct method
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Asymptotic equilibrium, periodic solutions, and Lyapunov's direct method (English)
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The author investigates conditions for an asymptotic equilibrium on the differential equation \(dx/dt=f(t,x),\;f\in C^{(0,1)}([T,\infty)\times \mathbb{R}^n,\mathbb{R}^n)\). He solves the problem by Lyapunov's direct method. In addition he considers an analogue of asymptotic equilibrium, which can be used in the theory of oscillations. It is reffered to as an equilibrium on an interval and plays an important role when finding periodic solutions.
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