ABSTRACT
It is probably the case that most of the scientific problems a mathematician might study are best described by nonlinear equations, while most of the existing mathematical theory applies to linear operators. This mismatch between mathematical information and scientific problems is gradually being overcome as we learn how to solve nonlinear problems. At present one of the best hopes of solving a nonlinear problem, or any problem for that matter, occurs if it is “close” to another problem we already know how to solve. We study the solution of the simpler problem and then try to express the solution of the more difficult problem in terms of the simpler one modified by a small correction.
