Advances in Difference Equations 
Volume 2006 (2006), Article ID 60860, 12 pages
doi:10.1155/ADE/2006/60860

Oscillation and nonoscillation for impulsive dynamic equations on certain time scales

Mouffak Benchohra,1 Samira Hamani,1 and Johnny Henderson2

 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

Abstract

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.