It's been a long time since I did any singular perturbations, but when I did, the text we used was [Kevorkian and Cole][1]; it definitely covers this type of problem. I think that Bender and Orszag's Advanced Mathematical Methods for Scientists and Engineers (sorry, MO won't let me add another link) has a section on it also, but not in as much depth. 

FWIW, I remember Bender and Orszag being a better book in general.

  [1]: http://www.amazon.com/Multiple-Singular-Perturbation-Mathematical-Sciences/dp/0387942025/ref=pd_sim_b_1