Inverse problems for differential equations on the half-line having a singularity in an interior point

Abstract

Arbitrary order ordinary dierential equations on the half-line having a nonintegrable singularity inside are studied under additional matching conditions for solutions at the singular point. We construct special fundamental systems of solutions for this class of dierential equations, study their asymptotical, analytical and structural properties and the behavior of the corresponding Stokes multipliers. These fundamental systems of solutions are used in spectral analysis of dierential operators with singularities. We study the inverse problem of recovering dierential equation from the given Weyl-Yurko matrix and prove the corresponding uniqueness theorem.