Nonlinear Functional Analysis (Dover Books on Mathematics)
| Author | : | |
| Rating | : | 4.22 (855 Votes) |
| Asin | : | 0486474410 |
| Format Type | : | paperback |
| Number of Pages | : | 464 Pages |
| Publish Date | : | 2014-08-20 |
| Language | : | English |
DESCRIPTION:
It offers extensive commentary and many examples in addition to an abundance of interesting, challenging exercises.Starting with coverage of the development of the Brower degree and its applications, the text proceeds to examinations of degree mappings for infinite dimensional spaces and surveys of monotone and accretive mappings. Subsequent chapters explore the inverse function theory, the implicit function theory, and Newton's methods as well as fixed-point theory, solutions to cones, and the Galerkin method of studying nonlinear equations. Suitable for graduate-level mathematics courses, this volume also serves as a reference for professionals.. Hailed as "eminently suitable as a text for a graduate course" by the Bulletin of the American Mathematical Society, this volume offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. The final chapters address extremal problems—including convexity, Lagrange multipliers, and mini-max theorems—and offer an introduction into bifurcation theory
A full treatment of the basics of non-linear FA, but short of examples. I found the text dense in the sense that each sentence carried a lot of information and required close reading. I also had to do quite a bit of additional work on most theorems and remarks. Don't expect to be hand held. This is not an elementary book but is a good introduction to the analytical, as opposed to topological, approach of degree theory.