## Existence results on the second-order nonconvex sweeping processes with perturbations.(English)Zbl 1048.49002

Summary: We prove several existence theorems for second-order differential inclusions of the form $$\dot x(t)\in K(x(t)), \ddot x(t)\in -N(K(x(t)); \dot x(t))+F(t,x(t),\dot x(t))$$, when $$K$$ and $$F$$ are two convex or nonconvex set-valued mappings taking their values in a Hilbert space.

### MSC:

 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) 49J52 Nonsmooth analysis 46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
Full Text: