Topics in Critical Point Theory

Provides an introduction to critical point theory and shows how it solves many difficult problems.

Kanishka Perera (Author), Martin Schechter (Author)

9781107029668, Cambridge University Press

Hardback, published 1 November 2012

167 pages
23.5 x 15.7 x 1.4 cm, 0.38 kg

'The authors have presented extremely powerful methods in critical point theory. It can be presumed that researchers in these subjects had been awaiting such an excellent source and here they have it. It is undoubtedly an excellent reference for research scientists in mathematics, physics and engineering.' Dhruba Adhikari, MAA Reviews

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 Fu?ík 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. Fu?ík spectrum
5. Jumping nonlinearities
6. Sandwich pairs
Appendix: Sobolev spaces
Bibliography
Index.

Subject Areas: Analytic topology [PBPH], Topology [PBP], Analytic geometry [PBMS], Geometry [PBM]