General existence results for third-order nonconvex state-dependent sweeping process with unbounded perturbations

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: - a (x (3) (t)) n (k (t,x (t)); a (x (t))) + f (t,x (t),x (t),x (t)) + g (x (t),x (t),x (t)) a. e. [ 0,t ],a (x (t)) k (t,x (t)),a.e. t [ 0,t ],x (0) = x 0,x (0) = u 0,x (0) = 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. © 2012 m. bounkhel and b. al-senan.