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.