Duality and perturbation methods in critical point theory / Nassif Ghoussoub.

Show other versions (1)

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined...

Full description

Bibliographic Details
Uniform Title:Cambridge tracts in mathematics ; 107.
Main Author: Ghoussoub, N. (Nassif), 1953- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 1993.
Series:Cambridge tracts in mathematics ; 107.
Subjects:
Critical point theory (Mathematical analysis)
Duality theory (Mathematics)
Perturbation (Mathematics)
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xviii, 258 pages) : digital, PDF file(s).
Variant Title:
Duality & Perturbation Methods in Critical Point Theory.
Format: Electronic eBook
Partial Contents:
  • Lipschitz and smooth perturbed minimization principles
  • Linear and plurisubharmonic perturbed minimization principles
  • The classical min-max theorem
  • A strong form of the min-max principle
  • Relaxed boundary conditions in the presence of a dual set
  • The critical set in the mountain pass theorem
  • Group actions and multplicity of critical points
  • The Palais-Smale condition around a dual set
  • examples
  • Morse indices of min-max critical points
  • the non degenerate case
  • Morse indices of min-max critical points
  • the degenerate case
  • Morse-tye informationon Palais-Smale sequences
  • Appendices.