Variational methods in nonlinear problems (Q2744051)

This excellent expository survey presents some of the main min-max methods developed in the last few decades. The results recalled in the paper are very useful because many nonlinear problems for partial differential equations arise as Euler equations for some appropriate problems in the Calculus of Variations. There are presented several celebrated results, such as Ekeland's Variational Principle, the Mountain Pass Lemma of Ambrosetti and Rabinowitz, the Linking theorem, and it is also discussed the role of the Palais-Smale compactness condition for finding critical points of energy functionals. The author concludes with an attempt to use the Mountain Pass lemma to solve the Jacobian conjecture, a long-standing problem in algebra.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00022].