Minimal trajectories of nonconvex differential inclusions (Q1103185)

We consider an optimization problem with endpoint constraints associated with a nonconvex differential inclusion. We give a necessary condition of the maximum principle type for a solution of the problem. Following the approach of the second author and \textit{St. Lojasiewicz} [Nonlinear Anal., Theory Methods Appl. 9, 109-130 (1985; Zbl 0557.49012)], the condition is stated in terms of single-valued selections of the convexified right-hand side of the inclusion.