Existence theorems for nth-order discontinuous ordinary differential inclusions

In this work an existence theorem for nth-order ordinary differential inclusions is proved without the continuity of multi-valued functions. Our results are an improvement upon the existence results of Dhage et al. [B.C. Dhage, T.L. Holambe, S.K. Ntouyas, Upper and lower solutions for second order discontinuous differential inclusions, Math. Sci. Res. J. 7 (5) (2003) 206–212] and Agarwal et al. [R.P. Agarwal, B.C. Dhage, D. O’Regan, The method of upper and lower solution for differential inclusions via a lattice fixed point theorem, Dynam. Systems Appl. 12 (2003) 1–7] under weaker conditions. c © 2006 Published by Elsevier Ltd