  In this paper, we provide an analytical study of the transmission eigenvalue
problem with two conductivity parameters. We will assume that the underlying
physical model is given by the scattering of a plane wave for an isotropic
scatterer. In previous studies, this eigenvalue problem was analyzed with one
conductive boundary parameter whereas we will consider the case of two
parameters. We will prove the existence and discreteness of the transmission
eigenvalues as well as study the dependence on the physical parameters. We are
able to prove monotonicity of the first transmission eigenvalue with respect to
the parameters and consider the limiting procedure as the second boundary
parameter vanishes. Lastly, we provide extensive numerical experiments to
validate the theoretical work.
