  This paper contains a lower bound of the Weyl type on the counting function
of the positive eigenvalues of the interior transmission eigenvalue problem
which justifies the existence of an infinite set of positive interior
transmission eigenvalues. We consider the classical transmission problem as
well as the case where the inhomogeneous medium contains an obstacle. One of
the essential components of the proof is an estimate for the D-t-N operator for
the Helmholtz equation for positive $\lambda$ that replaces the standard
parameter-elliptic estimate valid outside of the positive semi-axis.
