## 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

### Keywords:

Cauchy’s problem; Wintner’s criterion; global existence
Full Text: