General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations - M. Bounkhel; B. Al-Senan (Journal of Applied Mathematics)
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,ẋ(t));  A(ẍ(t)))+F(t,x(t),ẋ(t),ẍ(t))+G(x(t),ẋ(t),ẍ(t))      a.e.  [0,T], A(ẍ(t))∈K(t,ẋ(t)), a.e.    t∈[0,T], x(0)=x0,ẋ(0)=u0, ẍ(0)=υ0, 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.