singularity

Asymptotics of Solutions of Some Integral Equations Connected with Differential Systems with a Singularity

Authors: Ignatyev M. Y.

Our studies concern some aspects of scattering theory of the singular differential systems y ′ − x −1Ay − q(x)y = ρBy,
x  0 with n × n matrices A, B, q(x), x ∈ (0, ∞), where A, B are constant and ρ is a spectral parameter.
We concentrate on investigation of certain Volterra integral equations with respect to tensor-valued functions. The solutions of
these integral equations play a central role in construction of the so-called Weyl-type solutions for the original differential

Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

Authors: Senitsky Y. E.

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

SYSTEMS OF DIFFERENTIAL EQUATIONS ON THE LINE WITH REGULAR SINGULARITIES

Authors: Gorbunov O. V., Shieh C., Yurko V. A.

Non-selfadjoint second order differential systems on the line having a non-integrable regular singularity are studied. We construct special fundamental systems of solutions with prescribed analytic and asymptotic properties. Asymptotics of the corresponding Stockes multipliers is established.