An Introduction to Nonlinear Analysis

A 2005 guide to solving non-linear problems, using simple exposition and easy proofs.

Martin Schechter (Author)

9780521843973, Cambridge University Press

Hardback, published 10 January 2005

384 pages
23.4 x 16.2 x 2.2 cm, 0.73 kg

Review of the hardback: '… presents an introduction to critical point theory addressed to students with a modest background in Lebesgue integration and linear functional analysis. Many important methods from nonlinear analysis are introduced in a problem oriented way … well written … should be present in the library of any researcher interested in Lévy processes and Lie groups.' Zentralblatt MATH

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

1. Extrema
2. Critical points
3. Boundary value problems
4. Saddle points
5. Calculus of variations
6. Degree theory
7. Conditional extrema
8. Minimax methods
9. Jumping nonlinearities
10. Higher dimensions.

Subject Areas: Functional analysis & transforms [PBKF], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]