Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
18 January 2020 |
02 February 2020 |
10 March 2020 |
Abstract: We prove the existence of local solutions for upper semi-continuous non-convex differential inclusions, where the intersection between the right-hand side and the Clarke sub-differential of a regular function V is nonempty. This result is an extension of Bressan, Cellina and Colombo's work [3]. Furthermore, we have used the regularity of the function V to construct the approximate sequences. This construction is new and can be used to solve the viability problem for differential inclusions under weak assumptions.