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 to overcome difficulties when
applied to the theory of partial differential equations. Here,
Professor Ghoussoub describes a point of view that may help when
dealing with such problems. Building upon min-max methods, he
systematically develops a general theory that can be applied in a
variety of situations. In so doing he also presents a whole array
of duality and perturbation methods. The prerequisites for
following this book are relatively few; an appendix sketching
certain methods in analysis makes the book reasonably
self-contained. Consequently, it should be accessible to all
mathematicians, pure or applied, economists and engineers working
in nonlinear analysis or optimization.
General
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