Nonlinear Eigenvalue Problems Arising in Earthquake Initiation

We study a symmetric, nonlinear eigenvalue problem arising in earthquake initiation, and we establish the existence of inflnitely many solutions. Under the efiect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with respect to a prescribed topology. Our approach is based on nonsmooth critical-point theories in the sense of De Giorgi and Degiovanni.