Singularly perturbed problems with a turning point: The non-compatible case

Abstract

The singularly perturbed problems with a turning point were discussed in [21]. The case where the limit problem is compatible with the given data was fully resolved. However, with limited compatibility conditions on the data, the asymptotic expansions were constructed only up to the order of the level of compatibilities. In this paper, using a smooth cut-off function compactly supported around the turning point we resolve the difficulties incurred from the non-compatible data and finally provide the full asymptotic expansions up to any order.