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.
Author(s): Maria do Rosário Grossinho, Stepan Agop Tersian (auth.)
Series: Nonconvex Optimization and Its Applications 52
Edition: 1
Publisher: Springer US
Year: 2001
Language: English
Pages: 274
Tags: Partial Differential Equations; Difference and Functional Equations; Functional Analysis; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization
Front Matter....Pages i-xii
Minimization and Mountain-Pass Theorems....Pages 1-50
Saddle-Point and Linking Theorems....Pages 51-79
Applications to Elliptic Problems in Bounded Domains....Pages 81-111
Periodic Solutions for Some Second-Order Differential Equations....Pages 113-138
Dual Variational Method and Applications to Boundary Value Problems....Pages 139-172
Minimax Theorems for Locally Lipschitz Functionals and Applications....Pages 173-206
Homoclinic Solutions of Differential Equations....Pages 207-264
Back Matter....Pages 265-273
