Mutational inclusions: Differential inclusions in metric spaces

Abstract

The focus of interest is how to extend ordinary differential inclusions beyond the traditional border of vector spaces. We aim at an existence theorem for solutions whose values are in a given metric space. In the nineties, Aubin suggested how to formulate ordinary differential equations and their main existence theorems in metric spaces: mutational equations (which are quite similar to the quasidifferential equations of Panasyuk). Now the well-known Antosiewicz-Cellina Theorem is extended to so-called mutational inclusions. It provides new results about nonlocal set evolutions in R N .