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

Auteur principal : Kavian, Otared, 1952-, AuteurType de document : MonographieCollection : Mathématiques et applications, 13Langue : français.Pays: France.Éditeur : Paris : Springer-Verlag, 1993Description : 1 vol. (VIII-325 p.) ; 24 cmISBN: 2287004106.ISSN: 1154-483X.Bibliographie : Bibliogr. p. [311]-319. Index.Sujet MSC : 58-02, Research exposition (monographs, survey articles) pertaining to global analysis
47J05, Operator theory, Equations involving nonlinear operators
35J65, PDEs - Elliptic equations and elliptic systems, Nonlinear boundary value problems for linear elliptic equations
58E05, Global analysis, analysis on manifolds, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces
47-02, Research exposition (monographs, survey articles) pertaining to operator theory
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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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