Asymptotic Estimates of the Solution of a Singularly Perturbed Boundary Value Problem with an Initial Jump for Linear Differential Equations

摘要

The investigation of asymptotic properties of some singularly perturbed boundary value problems and the choice of an appropriate method for the construction of solutions or approximations to solutions often prove to be very difficult. An analysis shows that such problems include boundary value problems leading to infinitely large values of the solution at a discontinuity point as the small parameter tends to zero. Typically, there is an initial jump in such problems [1-3]. The most general results in this direction were obtained in [4-7].