  An new eigenvalue $\mathbb R$-linear problem arisen in the theory of
metamaterials is stated and constructively investigated for circular
non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced
when the radii of inclusions tend to zero. The nodal domains conjecture related
to univalent eigenfunctions is posed. Demonstration of the conjecture allows to
justify that a set of inclusions can be made neutral by surrounding it with an
appropriate coating.
