A degree-theoretic approach to parametric nonsmooth equations with multivalued perturbed solution sets

This paper studies the sensitivity of a parametric nonsmooth equation using degree theory and set-valued analysis. Under the assumption of existence of an approximating function of a certain kind, it investigates the existence, continuity, and differentiability of the set-valued solutions of the parametric equation. The present analysis is a synthesis of the work of several authors. Applications of the derived results to the convergence of Newton’s method and to the sensitivity analysis of parametric complementarity problems and variational inequalities will be discussed.