Existence results for discontinuous ordinary differential equations
by
J. Angel Cid
Universidade de Santiago de Compostela, Spain
Coauthors: Rodrigo L. Pouso

We prove the existence of Carathéodory solutions for initial value problems for systems of first order ordinary differential equations

x'(t)=f(t, x(t)) for a.e. I:=[t₀, t₀+L], x(t₀)=x₀ , (1)

where f:I ×R^m --> R^m may be discontinuous.

Our approach consists in passing from (1) to a solvable differential inclusion, and then we look for Carathéodory solutions of (1) among those of the inclusion. In this way we obtain new existence results for (1) as well as information about topological properties of the solution set.

Date received: May 28, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-17.