In this paper we study the variational method and integral equation methods
for a conical diffraction problem for imperfectly conducting gratings modeled
by the impedance boundary value problem of the Helmholtz equation in periodic
structures. We justify the strong ellipticity of the sesquilinear form
corresponding to the variational formulation and prove the uniqueness of
solutions at any frequency. Convergence of the finite element method using the
transparent boundary condition (Dirichlet-to-Neumann mapping) is verified. The
boundary integral equation method is also discussed