  We prove new existence results for a Nonlinear Helmholtz equation with
sign-changing nonlinearity of the form
  $$ - \Delta u - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}(\mathbb{R}^{N})
$$ with $k>0,$ $N \geq 3$, $p \in
\left[\left.\frac{2(N+1)}{N-1},\frac{2N}{N-2}\right)\right.$ and $Q \in
L^{\infty}(\mathbb{R}^{N})$. Due to the sign-changes of $Q$, our solutions have
infinite Morse-Index in the corresponding dual variational formulation.
