Families of regular solutions of singular systems

The seminal 1969 paper of W.A. Harris Jr., Y. Sibuya, and L. Weinberg provi ded new proofs for the Perron-Lettenmeyer theorem, as well as several other classical results, and has stimulated renewed consideration of families of regular solutions of certain singular problems. In this paper we give some further applications of the method developed there and, in addition, exami ne some connections between the Lettenmeyer theorem and an alternative theo rem which addresses a problem posed by H.L. Turrittin that dates back to an 1845 example of Briot and Bouquet.