Banachraum

I will first present a nonvanishing result for the Helmholtz resolvent operator in the spirit of Lions' first Lemma on concentration compactness. I will then focus on applications related to standing wave solutions of 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. If time permits, I will also discuss the concentration behavior of dual ground state solutions as the wave number tends to infinity.

Tobias Weth

Frankfurt