Dual variational methods and nonvanishing for the nonlinear Helmholtz equation

Gilles Evequoz, Tobias Weth

We set up a dual variational framework to detect real standing wave solutions of the nonlinear Helmholtz equation $$-\Delta u-k^{2}u=Q(x)|u{|}^{p-2}u,u\in W^{2,p}({\mathbb{R}}^N)$$…