On ordinary differential equations in Fréchet spaces. (Über gewöhnliche Differentialgleichungen in Frécheträumen.) (German) Zbl 0832.34055

Herzog, Gerd

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

Keywords:

Fréchet space; initial value problem; non-existence; uniqueness; Banach space