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

Lee, J. W.; O’Regan, D.

Ann. Pol. Math. 48, No. 3, 247-252 (1988).

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