Some results for differential inclusions in Banach spaces are given. Separability of the space is not assumed. The main results of the paper contain: the Filippov theorem, a relaxation theorem, results concerning continuous dependence of the solution sets on parameters and initial values and differentiability of the solution set.
The relaxation theorem for , , is proved under the following assumptions: 1) is measurable for each , has closed values. 2) is Lipschitz in the second variable. 3) For every continuous function , .
Then , where denotes the solution set for , and denotes the solution set for , .