Locally Lipschitz selections in Banach lattices

Let XX be a Banach space while (Y,⪯)(Y,⪯) is a Banach lattice. We consider the class of “upper separated” set-valued functions F:X→2YF:X→2Y and investigate the problem of the existence of convex and locally Lipschitz selections of FF. We discuss some applications of the selection results obtained in the paper to the theory of deterministic and stochastic differential inclusions.