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

Auteur: Kavian, Otared (1952-) - AuteurType de document: MonographieCollection: Mathématiques et applications ; 13Langue: françaisPays: FranceÉditeur: Paris : Springer-Verlag, 1993Description: 1 vol. (VIII-325 p.) ; 24 cm ISBN: 2287004106 ; br. Note: 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)Bibliographie: Bibliogr. p. [311]-319. Index. Sujets MSC: 58-02 Global analysis, analysis on manifolds -- Research exposition (monographs, survey articles)
47J05 Operator theory -- Equations and inequalities involving nonlinear operators -- Equations involving nonlinear operators (general)
35J65 Partial differential equations -- Elliptic equations and systems -- Nonlinear boundary value problems for linear elliptic equations
58E05 Global analysis, analysis on manifolds -- Variational problems in infinite-dimensional spaces -- Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
47-02 Operator theory -- Research exposition (monographs, survey articles)
Location Call Number Status Date Due
Couloir 11130-01 / Séries SMA (Browse Shelf) Available

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

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