Abstract In this paper we consider families of differential equations on some real interval that depend on a parameter ε, are regular for 0 ε ≠ 0 and have exactly one regular singular point for =0 ε = 0. Our aim is to give a formula which describes the asymptotic behavior of the solutions for 0 ε → 0. To this end, we use a method that combines matched asymptotic analysis with uniform asymptotic integration. We then apply our results to some typical examples, such as a differential equation with two coalescing regular singular points as well as a singular perturbation of the Bessel equation.
Harald Schmid (Fri,) studied this question.