| An Introduction to Minimax Theorems and Their Applications to Differential Equations 2001 Edition Contributor(s): Do Rosario Grossinho, Maria (Author), Tersian, Stepan Agop (Author) |
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ISBN: 0792368320 ISBN-13: 9780792368328 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: February 2001 Annotation: The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, 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 give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Medical - Mathematics | Mathematical Analysis |
| Dewey: 515.35 |
| LCCN: 00069629 |
| Series: Nonconvex Optimization and Its Applications |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.28 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. |