Extension of Beckert's Continuation Method to Variational Inequalities

A theoretical foundation is given for a recently proposed continuation method for parameter‐dependent nonlinear variational inequalities in Hilbert space. The second derivative of one of the functional in the inequality is assumed to generate a quadratic form that is equivalent to the norm of the Hilbert space. The value of this functional is used as continuation parameter. Existence of local continuations is shown using a generalization of Beckert's continuation method for eigenvalue equations and extending continuation results obtained recently by the nuthors. In addition, uniqueness and monotonicity results are proven for these continuations.