Advances in Difference Equations
Volume 2006 (2006), Article ID 60860, 12 pages
Oscillation and nonoscillation for impulsive dynamic equations on certain time scales
1Laboratoire de Mathématiques, Université de Sidi Bel Abbés, BP 89, Sidi Bel Abbés 22000, Algeria
2Department of Mathematics, Baylor University, Waco, Tx 76798-7328, USA
Received 1 December 2005; Revised 6 March 2006; Accepted 9 March 2006
Copyright © 2006 Mouffak Benchohra et al. 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.
We discuss the existence of oscillatory and nonoscillatory solutions for first-order impulsive
dynamic equations on time scales with certain restrictions on the points of impulse. We will rely on the nonlinear
alternative of Leray-Schauder type combined with a lower and upper solutions method.