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An Introduction to Minimax Theorems and Their Applications to Differential Equations - Couverture rigide
Synopsis
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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
- ÉditeurSpringer
- Date d'édition2001
- ISBN 10 0792368320
- ISBN 13 9780792368328
- ReliureRelié
- Langueanglais
- Nombre de pages274
- Coordonnées du fabricantnon disponible
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An Introduction to Minimax Theorems and Their Applications to Differential Equations (Nonconvex Optimization and Its Applications, 52)
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An Introduction to Minimax Theorems and Their Applications to Differential Equations
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Gebunden. Etat : New. Preface. 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 Applic. N° de réf. du vendeur 458441440
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An Introduction to Minimax Theorems and Their Applications to Differential Equations (Nonconvex Optimization and Its Applications, 52)
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An Introduction to Minimax Theorems and Their Applications to Differential Equations
Edité par
Springer Us Feb 2001, 2001
ISBN 10 : 0792368320
ISBN 13 : 9780792368328
Neuf
Couverture rigide
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Buch. Etat : Neu. Neuware - 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. N° de réf. du vendeur 9780792368328
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An Introduction to Minimax Theorems and Their Applications to Differential Equations (Nonconvex Optimization and Its Applications, 52)
Edité par
Springer, 2001
ISBN 10 : 0792368320
ISBN 13 : 9780792368328
Ancien ou d'occasion
Couverture rigide
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