Introduction à la théorie des points critiques et applications aux problèmes elliptiques / Otared Kavian

This book is intended as a higher level course in nonlinear analysis and its applications to differential equations. In the first chapter, the author revises a number of results on linear analysis and partial differential equations. He also extends some finite- dimensional results to infinite dimensions. In Chapter 2, he introduces the Brouwer degree in finite dimensions and the Leray-Schauder degree in infinite dimensions. He also gives some applications to nonlinear elliptic partial differential equations. In Chapter 3, he discusses critical point theory and applications. He also discusses Ky-Fan type theorems. In Chapter 4, he discusses constrained variational problems, including Ljusternik-Schnirelman theory. In Chapter 5, he discusses the variational problems which are not symmetric. He includes a discussion of perturbations of odd mappings and jumping nonlinearities. Lastly, in Chapter 6, he discusses variational problems where the Palais-Smale condition fails. (Zentralblatt)

Bibliogr. p. [311]-319. Index