IJPAM: Volume 10, No. 3 (2004)

SOME REMARKS ON GENERALIZED SOLUTIONS
OF DISCONTINUOUS DIFFERENTIAL EQUATIONS

Andrea Bacciotti
Department of Mathematics
Polytechnic of Turin
Corso Duca degli Abruzzi, 24
10129 Turin, ITALY
e-mail: andrea.bacciotti@polito.it


Abstract.In this paper we consider several concepts of generalized solutions for ordinary differential equations with a discontinuous right hand side. By means of some nontrivial examples, we show that Sentis solutions, forward-Euler solutions and Carathéodory solutions are independent notions.

Received: October 2, 2003

AMS Subject Classification: 34A38

Key Words and Phrases: discontinuous differential equations, Carathéodory solutions, Sentis solutions, forward-Euler solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 3