Stability of variational inequalities and prox-regularity in Hilbert space

In this paper we study the problem of stability of solutions of a classical variational inequality in a general Hilbert space. To do so, we use the concepts of local normal map and local natural map to transform the multi-valued problem into a single-valued one. Then we use the degree theory to obtain the stability result under some general hypotheses. Finally we discuss those hypotheses under different concepts of prox-regularity (local and uniform).