Solvability of a finite or infinite system of discontinuous quasimonotone differential equations

This paper proves the existence of solutions to the initial value problem [GRAPHICS] where f : [0, 1] x R-M --> R-M may be discontinuous but is assumed to satis fy conditions of superposition-measurability, quasimonotonicity, quasisemic ontinuity, and integrability. The set M can be arbitrarily large (finite or infinite); our theorem is new even for card(M) = 2. The proof is based par tly on measure-theoretic techniques used in one dimension under slightly st ronger hypotheses by Rzymowski and Walachowski. Further generalizations are mentioned at the end of the paper.