On the structure of the solution of singularly perturbed initial-boundary value problems with an unbounded spectrum of the limit operator

Summary (translated from the Russian): "We consider singularly perturbed initial-boundary value problems for some classes of linear systems of ordinary differential equations on the half-line with an unbounded spectrum of the limit operator. We present a new version of the proof of the existence of a unique and bounded solution as tto +0 for which, using the splitting method, we construct an asymptotic expansion, uniform on the entire half-line, and describe all the singularities (reflecting the structure of the corresponding boundary layers) in closed analytic form, including the critical case when the spectrum points of the limit operator may be tangent to the imaginary axis, which supplements previous results."