Second-order methods for some quasivariational inequalities

For quasivariational inequalities of special form in a Hilbert space, we construct a continuous second-order method and a discrete version of this method, prove the strong convergence of these methods, and indicate the possibility of obtaining estimates for the convergence rate. We separately study the convergence of the continuous method under the assumption that the operators describing the quasivariational inequality to be solved are potential. We establish sufficient conditions for the unique solvability of the nonlinear problems determining these methods.