Oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales

Mouffak Benchohra, Samira Hamani and Johnny Henderson

Address.
M. Benchohra, S. Hamani
Laboratoire de Mathematiques, Universite de Sidi Bel Abbes, BP 89, 22000 Sidi Bel Abbes, Algerie
J. Henderson, Department of Mathematics, Baylor University, Waco, Texas 76798-7328 USA

E-mail:
benchohra@univ-sba.dzr
hamani_samira@yahoo.fr
Johnny_Henderson@baylor.edu

Abstract. In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method.

AMSclassification. 34A37, 34A60, 39A12.

Keywords. Impulsive dynamic inclusion, oscillatory, convex valued multivalued, nonoscillatory, delta derivative, fixed point, time scale, upper and lower solutions.