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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications.
The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition.
Reviews
"Many, often difficult and advanced, examples included into the text form an excellent review of a frontline of actual research in the area. ... In conclusion, the reviewer may recommend the book of Zou and Schechter as an excellent reference for those seeking new as well as well-established techniques in the critical point theory approach to differential equations."
—Zentralblatt Math
"In many variational problems, the functional Phi is strongly indefinite and does not satisfy the Palais-Smale condition. In this book, the authors present some of the latest work which has been done to overcome these difficulties and prove the existence of critical points. They also show how the abstract results can be applied to many problems in ordinary and partial differential equations."
—Mathematical Reviews
Authors and Affiliations
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Tsinghua University, Beijing, China
Wenming Zou
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University of California, Irvine, USA
Martin Schechter
Bibliographic Information
Book Title: Critical Point Theory and Its Applications
Authors: Wenming Zou, Martin Schechter
DOI: https://doi.org/10.1007/0-387-32968-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2006
Hardcover ISBN: 978-0-387-32965-9Published: 13 June 2006
Softcover ISBN: 978-1-4419-4108-4Published: 29 October 2010
eBook ISBN: 978-0-387-32968-0Published: 10 September 2006
Edition Number: 1
Number of Pages: XII, 318
Topics: Analysis, Global Analysis and Analysis on Manifolds, Partial Differential Equations, Ordinary Differential Equations, Functional Analysis