Abstract: In this paper, we establish existence and uniqueness of
solutions for a class of inverse problems of degenerate differential
equations. The main tool is the perturbation theory for linear operators.
Abstract: In this paper we considered the Neumann problem for
the fourth order differential equation. First we define the weighted Sobolev space
2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution,
as well as give the description of the spectrum and of the domain of definition of the corresponding operator.
Abstract: A complete spectral representation for the
electromagnetic field of planar multilayered waveguides
inhomogeneously filled with omega media is presented. The problem
of guided electromagnetic propagation is reduced to an eigenvalue
equation related to a 2 ´ 2 matrix differential operator. Using the
concept of adjoint waveguide, general bi-orthogonality relations for
the hybrid modes (either from the discrete or from the continuous
spectrum) are derived. For the special case of homogeneous layers
the linear operator formalism is reduced to a simple 2 ´ 2 coupling
matrix eigenvalue problem. Finally, as an example of application, the
surface and the radiation modes of a grounded omega slab waveguide
are analyzed.