Differential inclusions with measurable-pseudo-Lipschitz right-hand side

Abstract

We obtain existence theorems and Filippov-Wazewski type relaxation theorems for differential inclusions in Banach spaces with measurable-pseudo-Lipschitz right-hand side. For the solution sets of these differential inclusions, we also describe some properties that extend classical theorems on continuous dependence and on differentiation of solutions with respect to initial data.