ON TURNING POINT PROBLEMS FOR SYSTEMS WITH ALMOST DIAGONAL COEFFICIENT MATRIX

摘要

The matrix P(x, ∈) has an asymptotic series in powers of ∈ with holomorphic coefficients. In the special case that the original dif-ferential equation was self-adjoint this property is preserved by the transformation. In the second chapter it is shown that in the case n = 2 the simplified system can be explicitly solved by asymptotic series that are uniformly valid in domainsnof the x-plane, independent of ∈, which contain the turning point x = 0. The terms of these series can be calculated by algebraic operations and quadratures.