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Topological transversality. Applications to initial-value problems. (English) Zbl 0674.34006

The authors give an interesting extension of the classical theorem of Wintner on the global existence of a solution y of the initial value problem \(y'=f(t,y)\), \(y(0)=r\) where \(f: [0,T]\times R^ n\to R^ n\) is continuous. This extension (which is actually a nonlocal existence theorem) is the best possible in the class of problems considered.
Reviewer: N.H.Pavel

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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