Multiple solutions for a class of elliptic equations with jumping nonlinearities

The paper deals with a semilinear elliptic Dirichlet problem with jumping nonlinearity and, using variational methods, it shows that the number of solutions tends to infinity as the number of jumped eigenvalues tends to infinity. In order to prove this fact, for every positive integer k it is proved that, when a parameter is large enough, there exists a solution which presents k interior peaks. The asymptotic behaviour and the profile of this solution, as the parameter tends to infinity, are also described.