Topics in Critical Point Theory

This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fucík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, p-Laplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research.

Preface; 1. Morse theory; 2. Linking; 3. Applications to semilinear problems; 4. Fucík spectrum; 5. Jumping nonlinearities; 6. Sandwich pairs; Appendix: Sobolev spaces; Bibliography; Index.

This book introduces the reader to powerful methods of analysis that can solve many problems. Written for graduate students and research scientists, it describes in detail, with examples, many of the topics that are useful in solving difficult problems, including Morse theory, critical groups and the minimax principle.

Kanishka Perera is Professor in the Department of Mathematical Sciences at Florida Institute of Technology.
Martin Schechter is Professor in the Department of Mathematics at the University of California, Irvine.