Abstract. We examine the main qualitative properties of the solution set of differential inclusion with the lag. The right-hand side is supposed to be one side Lipschitz and with almost continuous concex hull. Afterwards we prove the existence of solutions when the right-hand side is a sum of one side Lipschitz and almost (upper) semicontinuous multifunction, which satisfy compactness condition.
1991 Mathematics Subject Classification. 34A60, 34C99, 49J24, 49K24.
Key words and phrases. Functional differential inclusions, measure of noncompactness.