Advances in Difference Equations
Volume 2010 (2010), Article ID 650827, 20 pages
doi:10.1155/2010/650827
Research Article

Existence Theorems for First-Order Equations on Time Scales with Δ -Carathéodory Functions

Hugues Gilbert

Département de Mathématiques, Collège Édouard-Montpetit, 945 Chemin de Chambly, Longueuil, QC, J4H 3M6, Canada

Received 14 June 2010; Accepted 3 December 2010

Academic Editor: Kanishka Perera

Copyright © 2010 Hugues Gilbert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper concerns the existence of solutions for two kinds of systems of first-order equations on time scales. Existence results for these problems are obtained with new notions of solution tube adapted to these systems. We consider the general case where the right member of the system is Δ -Carathéodory and, hence, not necessarily continuous.