Differential Inclusions with Proximal Normal Cones in Banach Spaces

This paper is devoted to weaken "classical" assumptions and to give new arguments to prove existence of solutions of differential inclusions with proximal normal cones in Banach spaces. Mainly we define the concept of "directional prox-regularity" and give assumptions on a Banach space to ensure the existence of such differential inclusions (which permits to generalize existing results requiring a Hilbertian structure).