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- Title
A generalized Picard-Lindelöf theorem.
- Authors
Siegmund, Stefan; Nowak, Christine; Diblĺk, Josef
- Abstract
We generalize the Picard-Lindelöf theorem on the unique solvability of initial value problems by replacing the sufficient classical Lipschitz condition of f with respect to x = f(t,x), x(t0) = x0, by replacing the sufficient classical Lipschitz condition of f with respect to x with a more general Lipschitz condition along hyperspaces of the (t,x)-space. A comparison with known results is provided and the generality of the new criterion is shown by an example.
- Subjects
PICARD groups; NUMERICAL solutions to initial value problems; LIPSCHITZ spaces; MATHEMATICS theorems; HYPERSPACE; GENERALIZED position
- Publication
Electronic Journal of Qualitative Theory of Differential Equations, 2016, Issue 1-122, p1
- ISSN
1417-3875
- Publication type
Article
- DOI
10.14232/ejqtde.2016.1.28