Mild solutions of nonlinear evolution functional differential inclusions in Banach space (Q1422310)

In a Banach space, an abstract functional-differential inclusion with a multivalued operator \(A\) and multivalued functional perturbation \(F(t,\cdot)\) is considerd. Here, \(A\) is an operator such that \(A+\omega I\) is \(m\)-accretive for some \(\omega >0\) and the multimapping \(F(t,\cdot)\) with closed bounded values is Lipschitzian with respect to the Hausdorff metric. By using the well-known Filippov technique, the existence of a mild solution of this inclusion is proved. The result is applied to a nonlinear functional control problem.