An Introduction to Minimax Theorems and Their Applications to Differential Equations (Nonconvex Optimization and Its Applications)

Do Rosário Grossinho, Maria Do Rosario; Tersian, Stepan Agop

ISBN 10: 144194849X / ISBN 13: 9781441948496

Editore: Springer, 2010

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Dati bibliografici

• Titolo: An Introduction to Minimax Theorems and Their Applications to Differential Equations (Nonconvex Optimization and Its Applications)
• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 144194849X
• ISBN 13: 9781441948496
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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 Applications. 6. Minimax Theorems for Locally Lipschitz Functionals and Applications. 7. Homoclinic Solutions of Differential Equations. Notations. Index.