An Introduction to Minimax Theorems and Their Applications to Differential Equations
Seiten
2001
|
2001 ed.
Kluwer Academic Publishers (Verlag)
978-0-7923-6832-8 (ISBN)
Kluwer Academic Publishers (Verlag)
978-0-7923-6832-8 (ISBN)
This text is intended to be an introduction to critical point theory and its applications to differential equations. Its goals include: presenting a survey of existing minimax theorems; and giving applications to elliptic differential equations in bounded domains.
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.
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 | 28.2.2001 |
|---|---|
| Reihe/Serie | Nonconvex Optimization and Its Applications ; 52 |
| Zusatzinfo | XII, 274 p. |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-7923-6832-0 / 0792368320 |
| ISBN-13 | 978-0-7923-6832-8 / 9780792368328 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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