An Introduction to Minimax Theorems and Their Applications to Differential Equations / Edition 1

by Maria do Rosário Grossinho, Stepan Agop Tersian

Overview

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.

Product Details

ISBN-13:	9781441948496
Publisher:	Springer US
Publication date:	12/02/2010
Series:	Nonconvex Optimization and Its Applications , #52
Edition description:	Softcover reprint of hardcover 1st ed. 2001
Pages:	274
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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.

Editorial Reviews

Written for graduate and post-graduate students, this introduction to critical point theory and its applications to differential equations offers a survey of existing minimax theories. It also gives applications to elliptic differential equations in bounded domains and considers the dual variational method for problems with continuous and discontinuous nonlinearities. Specific attention is given to locally Lipschitz functionals and applications to fourth-order differential equations with discontinuous nonlinearities. Grossinho teaches at Universidade Tcnica de Lisboa. Tersian teaches at the University of Rousse. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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