Compatible and Incompatible Nonuniqueness Conditions for the Classical Cauchy Problem
In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem x˙=f(t,x), x(t0)=x0 are given. As the essential tool serves a method which estimates the “distance” between two solutions with an appropriate Lyapunov function and permits to show that under certa...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/743815 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In the first part of this paper sufficient conditions for nonuniqueness of the classical
Cauchy problem x˙=f(t,x), x(t0)=x0 are given. As the essential tool serves a
method which estimates the “distance” between two solutions with an appropriate
Lyapunov function and permits to show that under certain conditions the “distance” between two different solutions vanishes at the initial point. In the second part attention
is paid to conditions that are obtained by a formal inversion of uniqueness
theorems of Kamke-type but cannot guarantee nonuniqueness because they are incompatible. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |