On first order impulsive semilinear functional differential inclusions

M. Benchohra, J. Henderson and S. K. Ntouyas

E-mail: sntouyas@cc.uoi.gr

Abstract. In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined
with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive
semilinear functional differential inclusions in Banach spaces.

AMSclassification. 34A37, 34A60, 34G20, 35R10.

Keywords. Initial value problem, impulsive functional differential inclusions, convex multivalued map, fixed point, mild solution.