Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Ordinary differential equations and systems with time-dependent discontinuity sets

J. Ángel Cida1 and Rodrigo L. Pousoa2

a1 Departamento de Análise Matemática, Facultade de Matemáticas, Campus Sur, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain angelcid@usc.es

a2 Departamento de Análise Matemática, Facultade de Matemáticas, Campus Sur, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain rodrigolp@usc.es

Abstract

In this paper we prove new existence results for non-autonomous systems of first order ordinary differential equations under weak conditions on the nonlinear part. Discontinuities with respect to the unknown are allowed to occur over general classes of time-dependent sets which are assumed to satisfy a kind of inverse viability condition.

(Received July 10 2003)

(Accepted March 01 2004)