| An Introduction to Minimax Theorems and Their Applications to Differential Equations Contributor(s): Do Rosario Grossinho, Maria (Author), Tersian, Stepan Agop (Author) |
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ISBN: 144194849X ISBN-13: 9781441948496 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Functional Analysis - Mathematics | Applied |
| Dewey: 515.35 |
| Series: Nonconvex Optimization and Its Applications |
| Physical Information: 0.7" H x 6.1" W x 9" (0.90 lbs) 274 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |