Résumé en anglais

We show, by variational methods, that there exists a set A open and dense in {a ∈ L∞(RN) : liminf|x|→∞ a(x) ≥ 0} such that if a ∈ A then the problem −∆u + u = a(x)|u| p−1u, u ∈ H1(RN), with p subcritical (or more general nonlinearities), admits infinitely many solutions.