Nonlinear differential equations is hard to find good references on-partly due to the difficulty of the subject and partly due to the highly specialized nature of most of the research problems connected with them. But a lot of these problems are really problems of numerical approximation-so I think you'll have greater luck if you begin searching the literature on THAT,math.

A very good book to start with that has a lot of great material on this is Atkinson and Kan's *Theoretical Numerical Analysis*. Not only is it terrifically written and comprehensive with lots of examples,it's one of the most scholarly texts I've ever seen with **complete and opiniated** references. I think you'll find this book's references will give you a great deal of direction for further study on nonlinear solution of ODE's.

An older book that has a lot of nice material on power series and other numerical methods for ODE's is Einar Hille's *Lectures On Ordinary Differential Equations*. Why most of Hille's texts-which are all wonderful-are out of print mystifies me.

That should help you get started,especially the Atkinson/Han book. Good hunting!