  In this paper we study nonlinear Helmholtz equations with sign-changing
diffusion coefficients on bounded domains. The existence of an orthonormal
basis of eigenfunctions is established making use of weak T-coercivity theory.
All eigenvalues are proved to be bifurcation points and the bifurcating
branches are investigated both theoretically and numerically. In a
one-dimensional model example we obtain the existence of infinitely many
bifurcating branches that are mutually disjoint, unbounded, and consist of
solutions with a fixed nodal pattern.
