The Mountain Pass Theorem: Variants, Generalizations and Some Applications
The book presents various aspects of the famous Mountain Pass Theorem (by Ambrosetti and Rabinowitz) as one of the most powerful tools in variational methods in nonlinear analysis. From the very beginning the reader is led from the easily accessible results of the variational principles on almost critical points, through the finite dimensional considerations to more complicated ones. We learn about standard topics (classical and dual Mountain Pass Theorem, topological index theory, the role of symmetry) as well as the more or less non-standard techniques (the non smooth and/or geometrically constrained Mountain Pass Theorem). The question of numerical approaches is also touched. The book will be valuable both for specialists and graduate students starting their scientific career in the field. However, the style of writing is clear and concise, and therefore the book can be recommended also as a first reading to members of broad mathematical community wanting to get some knowledge of the field.