On uniqueness criteria for systems of ordinary differential equations (Q1399317)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On uniqueness criteria for systems of ordinary differential equations |
scientific article; zbMATH DE number 1956860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On uniqueness criteria for systems of ordinary differential equations |
scientific article; zbMATH DE number 1956860 |
Statements
On uniqueness criteria for systems of ordinary differential equations (English)
0 references
30 July 2003
0 references
A local equivalence between two initial value problems is used to prove a uniqueness criterion for the classical Cauchy problem. Moreover, a version of Lipschitz's uniqueness criterion is generalized. Finally, it is proved that continuity implies local uniqueness for a class of two-dimensional autonomous systems, which includes the Hamiltonian ones, provided that the initial condition is not a critical point.
0 references
initial value problems
0 references
uniqueness criteria
0 references
local equivalence
0 references
