An Introduction to Minimax Theorems and Their Applications to Differential Equations

Maria do Rosário Grossinho, Stepan Agop Tersian (Autoren)

Buch | Softcover

274 Seiten

2010 | 1st ed. Softcover of orig. ed. 2001
Springer-Verlag New York Inc.
978-1-4419-4849-6 (ISBN)

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This text is meant to be an introduction to critical point theory and its ap- plications to differential equations. It is designed for graduate and postgrad- uate students as well as for specialists in the fields of differential equations, variational methods and optimization. Although related material can be the treatment here has the following main purposes: found in other books, * To present a survey on existing minimax theorems, * To give applications to elliptic differential equations in bounded do- mains and periodic second-order ordinary differential equations, * To consider the dual variational method for problems with continuous and discontinuous nonlinearities, * To present some elements of critical point theory for locally Lipschitz functionals and to give applications to fourth-order differential equa- tions with discontinuous nonlinearities, * To study homo clinic solutions of differential equations via the varia- tional method. The Contents of the book consist of seven chapters, each one divided into several sections. A bibliography is attached to the end of each chapter.
In Chapter I, we present minimization theorems and the mountain-pass theorem of Ambrosetti-Rabinowitz and some of its extensions. The con- cept of differentiability of mappings in Banach spaces, the Fnkhet's and Gateaux derivatives, second-order derivatives and general minimization the- orems, variational principles of Ekeland [EkI] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais-Smale conditions and mountain-pass theorems are consid- ered.

1. Minimization and Mountain-Pass Theorems.- 2. Saddle-Point and Linking Theorems.- 3. Applications to Elliptic Problems in Bounded Domains.- 4. Periodic Solutions for Some Second-Order Differential Equations.- 5. Dual Variational Method and Applications.- 6. Minimax Theorems for Locally Lipschitz Functionals and Applications.- 7. Homoclinic Solutions of Differential Equations.- Notations.

Erscheint lt. Verlag	2.12.2010
Reihe/Serie	Nonconvex Optimization and Its Applications ; 52
Zusatzinfo	XII, 274 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-4419-4849-X / 144194849X
ISBN-13	978-1-4419-4849-6 / 9781441948496
Zustand	Neuware