On set differential equations in Banach spaces - a second type Hukuhara differentiability approach

In this paper we consider set differential equations in Banach spaces and with the second type Hukuhara derivative. We show that a sequence of successive approximations converges uniformly to a unique local solution of a Cauchy problem. Some comparison results are formulated and a continuity of solution with respect to equation data is shown. The existence of a global solution is also established.