Existence results for second order convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces

摘要

In a previous work the authors proved under a complex assumption on the set-valued mapping, the existence of Lipschitz solutions for second order convex sweeping processes in $p$-uniformly smooth and $q$-uniformly convex Banach spaces. In the present work we prove the same result, under a condition on the distance function to the images of the set-valued mapping. Our assumption is much simpler than the one used in the former paper.