AN EXISTENCE RESULT FOR FIRST ORDER INITIAL VALUE PROBLEMS FOR IMPULSIVE DIFFERENTIAL INCLUSIONS IN BANACH SPACES

Mouffak Benchohra and Abdelkader Boucherif

Address. Mouffak Benchohra, Departement de Mathematiques, Universite de Sidi Bel Abbes, BP 89, 22000 Sidi Bel Abbes, ALGERIE

Abdelkader Boucherif, Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, B.O. Box 5046 Dahran 31261, SAUDI ARABIA

E-mail: benchohra@yahoo.com, aboucher@kfupm.edu.sa

Abstract. In this paper, a nonlinear alternative for multivalued maps is used to investigate the existence of solutions of first order impulsive initial value problem for differential inclusions in Banach spaces.

AMSclassification. 34A37, 34A60, 34G20

Keywords. Impulsive initial value problem, multivalued map, a priori bounds, existence, fixed point.