Nonlinear Analysis and Semilinear Elliptic Problems
Published on 4. January 2007
Book
Hardback
328 pages
978-0-521-86320-9 (ISBN)
Description
Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.
Reviews / Votes
'In the reviewer's opinion, this book can serve very well as a textbook in topological and variational methods in nonlinear analysis. Even researchers working in this field might find some interesting material (at least the reviewer did).' Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 55 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 22 mm
Weight
630 gr
ISBN-13
978-0-521-86320-9 (9780521863209)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Antonio Ambrosetti | Andrea Malchiodi
Nonlinear Analysis and Semilinear Elliptic Problems
E-Book
03/2007
1st Edition
Cambridge University Press
€79.99
Available for download
Persons
Antonio Ambrosetti is a Professor at SISSA, Trieste. Andrea Malchiodi is an Associate Professor at SISSA, Trieste.
Content
Preface; 1. Preliminaries; Part I. Topological Methods: 2. A primer on bifurcation theory; 3. Topological degree, I; 4. Topological degree, II: global properties; Part II. Variational Methods, I: 5. Critical points: extrema; 6. Constrained critical points; 7. Deformations and the Palais-Smale condition; 8. Saddle points and min-max methods; Part III. Variational Methods, II: 9. Lusternik-Schnirelman theory; 10. Critical points of even functionals on symmetric manifolds; 11. Further results on Elliptic Dirichlet problems; 12. Morse theory; Part IV. Appendices: Appendix 1. Qualitative results; Appendix 2. The concentration compactness principle; Appendix 3. Bifurcation for problems on Rn; Appendix 4. Vortex rings in an ideal fluid; Appendix 5. Perturbation methods; Appendix 6. Some problems arising in differential geometry; Bibliography; Index.