The study of critical points has grown rapidly and has led to new applications in many scientific fields. This monograph covers the latest in the field. Topics include semilinear problems, Fucik spectrum, elliptic systems, sandwich pairs and more.

Many problems in science and engineering involve the solution of differential equations or systems. One of most successful methods of solving nonlinear equations is the determination of critical points of corresponding functionals. The study of critical points has grown rapidly in recent years and has led to new applications in other scientific disciplines. This monograph continues this theme and studies new results discovered since the author's preceding book entitled Linking Methods in Critical Point Theory.

Written in a clear, sequential exposition, topics include semilinear problems, Fucik spectrum, multidimensional nonlinear wave equations, elliptic systems, and sandwich pairs, among others. With numerous examples and applications, this book explains the fundamental importance of minimax systems and describes how linking methods fit into the framework.

Minimax Systems and Critical Point Theory is accessible to graduate students with some background in functional analysis, and the new material makes this book a useful reference for researchers and mathematicians.

Review of the author's previous Birkhäuser work, Linking Methods in Critical Point Theory:

The applications of the abstract theory are to the existence of (nontrivial) weak solutions of semilinear elliptic boundary value problems for partial differential equations, written in the form Au = f(x, u). . . . The author essentially shows how his methods can be applied whenever the nonlinearity has sublinear growth, and the associated functional may increase at a certain rate in every direction of the underlying space. This provides an elementary approach to such problems. . . . A clear overview of the contents of the book is presented in the first chapter, while bibliographical comments and variant results are described in the last one. -MathSciNet

The study of critical points has grown rapidly in recent years, finding applications in most every science. This book spans the material required for those who want a survey of modern critical point theory.

Key features:

*Provides an introduction to linking methods and generalizations

*Explains the fundamentals of minimax systems

*Many examples and applications

This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.