ONA SPECTRAL VARIATIONAL PROBLEM ARISING IN THE STUDYOF EARTHQUAKES Multiplicity and perturbation from symmetry

Abstract We consider an eigenvalue variational inequality problem arising in the earthquake initiation. Our purpose is twofold. Firstly, in the symmet-ric case, we establish the existence of infinitely many distinct solutions. Next, in the case where the problem is affected by a non-symmetric perturbation, we prove that the number of solutions of the perturbed problem becomes larger and larger if the perturbation “tends ” to zero with respect to a suitable topology. Since the canonical energy func-tionals are included neither in the theory of monotone operators, nor in their Lipschitz perturbations, the proofs of the main results rely on non-smooth critical point theories in the sense of De Giorgi and Degiovanni combined with methods from algebraic topology