Real solutions to the nonlinear Helmholtz equation with local nonlinearity

Gilles Evequoz, Tobias Weth

In this paper, we study real solutions of the nonlinear Helmholtz equation $$-\Delta u-k^{2}u=f(x,u),x\in {\mathbb{R}}^N$$ satisfying the asymptotic conditions $$ u(x)=O(|x|^{\frac{1-…