Electron. J. Diff. Eqns., Vol. 2001(2001), No. 32, pp. 1-19.

Cauchy problem for derivors in finite dimension

Jean-François Couchouron, Claude Dellacherie, & Michel Grandcolas

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.

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Jean-Francois Couchouron
UFR MIM Departement de Mathematiques
Universite de Metz
Ile du Saulcy
57045 Metz Cedex 01 France
e-mail: couchour@loria.fr
Dellacherie Claude
Departement de Mathematiques
UFR Sciences, Site Colbert, Universite de Rouen
76821 Mont Saint Aignan, france
e-mail: dellache@univ-rouen.fr
Michel Grandcolas
UFR MIM Departement de Mathematiques
Universite de Metz
Ile du Saulcy
57045 Metz Cedex 01 France
e-mail: grandcol@poncelet.univ-metz.fr

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