Critical Point Theory and Its Applications

Wenming Zou, Martin Schechter

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English

Springer Verlag
01 June 2006

Mathematics & Sciences; Calculus & mathematical analysis

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.

By: Wenming Zou, Martin Schechter
Imprint: Springer Verlag
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm, Spine: 19mm
Weight: 1.420kg
ISBN: 9780387329659
ISBN 10: 038732965X
Pages: 332
Publication Date: 01 June 2006
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Preliminaries.- Functionals Bounded Below.- Even Functionals.- Linking and Homoclinic Type Solutions.- Double Linking Theorems.- Superlinear Problems.- Systems with Hamiltonian Potentials.- Linking and Elliptic Systems.- Sign-Changing Solutions.- Cohomology Groups.

Reviews for Critical Point Theory and Its Applications

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