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On ordinary differential equations in Fréchet spaces. (Über gewöhnliche Differentialgleichungen in Frécheträumen.) (German) Zbl 0832.34055
Karlsruhe: Math. Fak., Univ. Karlsruhe, 65 S. (1992).
Let $$F$$ be a real Fréchet space and denote by $$f: [0, T]\times F\to F$$ a continuous mapping. The author considers the initial value problem $$(*)$$ $$y'(t)= f(t, y(t))$$, $$y(0)= y_0\in F$$ in $$F$$ and investigates the existence and non-existence as well as the uniqueness problems to $$(*)$$. The difference to corresponding results in the Banach space case is pointed out.
Reviewer: R.Manthey (Jena)

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations