Abstract
In this paper we prove the existence of solutions to the following third order differential inclusion:
{x((3))(t) is an element of F(t, x(t), (x) over dot (t), (sic) (t)) + G(x(t), (x) over dot (t), (sic) (t)), a.e. on [0, T] x(0) = x(0), (x) over dot(0) = u(0), (sic)(0) = v(0), and (sic)(t) is an element of S, for all t is an 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) subset of partial derivative(C) g(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.