| Abstract: | This is a continuation of our earlier article concerning the boundary-value problem  where A , B are prescribed constants, and 0 < ε ≪ 1 is a small positive parameter. In that article, we assumed the coefficients a ( x ) and b ( x ) are sufficiently smooth functions with the behavior given by a ( x ) ∼ αx and b ( x ) ∼ β as x → 0, where α > 0 and β / α ≠ 1, 2, 3,…. In the present article, we are concerned with the case α < 0 and β / α ≠ 0, −1, −2,…. An asymptotic solution is obtained for the problem, which holds uniformly for all x in x −, x +]. Our result is proved rigorously, and shows that a previous result in the literature is incorrect. |
