Nonlinear Elliptic Eigenvalue Problems with Discontinuities

In this paper we study the existence of solution for two different eigenvalue problems. The first is nonlinear and the second is semilinear. Our approach is based on results from the nonsmooth critical point theory. In the first theorem we prove the existence of at least two nontrivial solutions when l is in a half-axis. In the second theorem based on a nonsmooth variant of the generalized mountain pass theorem., we prove the existence of at least one nontrivial solution for every l gR.