In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity $F$ admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

Keywords: Functional impulsive differential inclusions, measurable selection, condensing multi-valued map