General Existence Results for Nonconvex Third Order Differential Inclusions

In this paper we prove the existence of solutions to the following third order differential inclusion: {x(3)(t) element of F(t,x(t),x-dot (t),x-dotdot (t)) + G(x(t),x-dot(t),x-dotdot(t)), a.e. on [0,T] x(0) = x0,x-dot(0) = u0,x-dotdot (0) = v0, and x-dotdot(t) element of S,for every t element of [0,T], where F : [0,T] x H x H x H → H is a continuous set-valued mapping, G : H x H x H → H is an upper semi-continuous set-valued mapping with G(x,y,z) is contained in ∂Cg(z) where g : H → R is a uniformly regular function over S and locally Lipschitz and S is a ball compact subset of a separable Hilbert space H. (author)