I will discuss a nonvanishing result for the Helmholtz resolvent operator in the spirit of Lions' first Lemma on concentration compactness. The result will be applied to prove the existence of standing wave solutions to nonlinear Helmholtz equations with power type nonlinearities. To detect these solutions, we need to set up a dual variational framework. Classical direct methods in critical point theory do not apply to this problem due to the lack of Fredholm properties. This is joint work with Gilles Evequoz.