This 2003 book presents min-max methods through a study of the
different faces of the celebrated Mountain Pass Theorem (MPT) of
Ambrosetti and Rabinowitz. The reader is led from the most
accessible results to the forefront of the theory, and at each step
in this walk between the hills, the author presents the extensions
and variants of the MPT in a complete and unified way. Coverage
includes standard topics, but it also covers other topics covered
nowhere else in book form: the non-smooth MPT; the geometrically
constrained MPT; numerical approaches to the MPT; and even more
exotic variants. Each chapter has a section with supplementary
comments and bibliographical notes, and there is a rich
bibliography and a detailed index to aid the reader. The book is
suitable for researchers and graduate students. Nevertheless, the
style and the choice of the material make it accessible to all
newcomers to the field.
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