The Mountain Pass Theorem

Description

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.

First Sentence

Variational and topological methods have proved to be powerful tools in the resolution of concrete nonlinear boundary value problems appearing in many disciplines where classical methods may fail.

Subjects

Other Editions

• The Mountain Pass Theorem: Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications)HardcoverCambridge University Press2003-09-15
• Mountain Pass TheoremCambridge University Press2003-01-01
• Mountain Pass TheoremCambridge University Press2003-01-01
• Mountain Pass TheoremCambridge University Press2003-01-01
• Mountain Pass TheoremCambridge University Press2003-01-01
• Mountain Pass TheoremCambridge University Press2004-01-01