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Erschienen in:
1981 | OriginalPaper | Buchkapitel
Nonautonomous Ordinary Differential Equations
verfasst von : Stephen H. Saperstone
Erschienen in: Semidynamical Systems in Infinite Dimensional Spaces
Verlag: Springer New York
Enthalten in: Professional Book Archive
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The solutions of the autonomous ordinary differential equation 1.1$$ \dot{x} = f(x) $$ (where ẋ stands for dx/dt) give rise to a semidynamical (even dynamical) system on IRd provided f: W → IRd is continuous on the open subset W ⊂ IRd and the solutions of Equation (1.1) through any point (x0,t0) ∈ W × IR are uniquely defined and remain in W for all time. In fact, if Φ(x0;t) denotes the solution of Equation (1.1) through (x0,0) evaluated at time t ∈ IR+, it can be verified that (W,Φ) is a semidynamical system.