An Introduction to Minimax Theorems and Their Applications to Differential Equations
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An Introduction to Minimax Theorems and Their Applications to Differential Equations

An Introduction to Minimax Theorems and Their Applications to Differential Equations


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About the Book

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.


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Product Details
  • ISBN-13: 9781441948496
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: Softcover reprint of hardcover 1st ed. 2001
  • Language: English
  • Returnable: Y
  • Spine Width: 18 mm
  • Width: 155 mm
  • ISBN-10: 144194849X
  • Publisher Date: 02 Dec 2010
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 274
  • Series Title: Nonconvex Optimization and Its Applications
  • Weight: 458 gr


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