Abstract
Abstract Singularly perturbed boundary value problems with unbounded boundary values arise in first-order catalytic reactions, as well Cauchy problems associated with boundary layer phenomena. In this paper, we develop an algorithm for constructing an asymptotic expansion of the solution to a singularly perturbed two-point boundary value problem with an unbounded boundary condition. A remainder term theorem is proved. Based on the constructed asymptotic expansion, we prove the assertion that the solution to the original boundary value problem passes to the limit solution of the degenerate problem as a small parameter tends to zero. It was found that the solution of the original singularly perturbed two-point boundary value problem with an unbounded boundary condition exhibits a zero-order jump phenomenon.