Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 32, pp. 1-19.
Title: Cauchy problem for derivors in finite dimension
Authors: Jean-Francois Couchouron (Univ. de Metz, France)
Claude Dellacherie (Univ. de Rouen, France)
Michel Grandcolas (Univ. de Metz, France)
Abstract:
In this paper we study the uniqueness of solutions to
ordinary differential equations which fail to satisfy
both accretivity condition and the uniqueness condition of
Nagumo, Osgood and Kamke.
The evolution systems considered here are governed by a
continuous operators $A$ defined on $\mathbb{R}^N$ such that
$A$ is a derivor; i.e., $-A$ is quasi-monotone with respect
to $(\mathbb{R}^{+})^N$.
Submitted December 4, 2000. Published May 8, 2001.
Math Subject Classifications: 34A12, 34A40, 34A45, 34D05.
Key Words: derivor; quasimonotone operator; accretive operator;
Cauchy problem; uniqueness condition.