Search

We study a class of eigenvalue problems relative to variational inequalities and we give sufficient conditions for the existence of solutions. We apply the results to some differential equations problems.

Let Ω be an open bounded set in Rm and let EΩ be an elliptic self-adjoint variational operator with Dirichlet's data zero. Changing suitably the shape of Ω, we obtain a new open set Ω* such that EΩ* has only simple eigenvalues. Moreover choosing a suitable metric for the family of the open sets diffromorphic to Ω, the set of all Ω* such that EΩ* has multiple eigenvalues, is of the first category.