differential systems

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

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

SYSTEMS OF DIFFERENTIAL EQUATIONS ON THE LINE WITH REGULAR SINGULARITIES

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.