Perturbation from Dirichlet problem involving oscillating nonlinearities

In this paper we prove that if the potential has a suitable oscillating behavior in any neighborhood of the origin (respectively +∞), then under very mild conditions on the perturbation term g, for every there exists bk>0 such that has at least k distinct weak solutions in , for every with λ bk. Moreover, information about the location of such solutions is also given. In fact, there exists a positive real number σ>0, which does not depend on λ, such that the -norm of each of those k solutions is not greater than σ.