Appendix. Local Nonlinear Analysis

Abstract

In many of the problems treated in this text, we have detailed information about special solutions, especially those termed trivial. We can often determine solutions in a neighborhood of the special solutions or determine solutions of problems with nearby data by using methods relying on versions of the Implicit Function Theorem. In this chapter we develop these methods of local nonlinear analysis. Each of our results is a consequence of the Contraction Mapping Principle, which we now state and prove.