Abstract
We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: -A (x((3)) (t)) is an element of N(K(t, (x) over dot(t)); A ((sic)(t))) + F(t, x(t), (x) double over dot(t), (sic)(t)) + G(x(t), (x) over dot(t)), (sic)(t)) a.e. [0, T], A(sic)(t)) is an element of K(t, (x) over dot(t)), a.e. t is an element of [0, T], x(0) = x(0), (x) over dot(0) = u(0), (sic)0 = upsilon(0), where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-valued mapping, and G is an unbounded uniformly continuous nonconvex set-valued mapping in a separable Hilbert space H.