Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem

Abstract

The implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a (possibly infinite-dimensional) parameter. In this way, results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions. The abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions (Schrödinger operator with the potential as the parameter).