An Introduction to Nonlinear Analysis

Martin Schechter (University of California, Irvine)

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English

Cambridge University Press
13 September 2012

Calculus & mathematical analysis; Non-linear science

Series: Cambridge Studies in Advanced Mathematics

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.

By: Martin Schechter (University of California Irvine)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 95
Dimensions: Height: 229mm, Width: 152mm, Spine: 22mm
Weight: 560g
ISBN: 9780521605137
ISBN 10: 052160513X
Series: Cambridge Studies in Advanced Mathematics
Pages: 382
Publication Date: 13 September 2012
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Replaced By: 9780521843973
Format: Paperback
Publisher's Status: Active

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.

Reviews for An Introduction to Nonlinear Analysis

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