Lower semicontinuous differential inclusions. One-sided Lipschitz approach
Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in . Using the main idea of , we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.