The Mountain Pass Theorem: Variants, Generalizations and Some ApplicationsCambridge University Press, 15.09.2003 This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field. |
Inhalt
1 | |
Obtaining Almost Critical Points Variational Principle | 22 |
Obtaining Almost Critical Points The Deformation Lemma | 33 |
Comments and Additional Notes | 41 |
The Finite Dimensional | 49 |
The Topological | 57 |
The Classical MPT | 65 |
Comments and Additional Notes | 76 |
The Nonsmooth MPT | 174 |
The Metric MPT | 186 |
The MPT on Convex Domains | 207 |
MPT in Order Intervals | 216 |
The Linking Principle | 226 |
The Intrinsic MPT | 240 |
Geometrically Constrained MPT | 248 |
Numerical MPT Implementations | 259 |
The Multidimensional MPT | 81 |
The Limiting Case in the MPT | 93 |
PalaisSmale Condition versus Asymptotic Behavior | 103 |
Symmetry and the MPT | 114 |
The Structure of the Critical Set in the MPT | 134 |
Weighted PalaisSmale Conditions | 149 |
The Semismooth MPT | 163 |
Perturbation from Symmetry and the MPT | 275 |
Applying the MPT in Bifurcation Problems | 288 |
More Climbs | 296 |
A Background Material | 315 |
Bibliography | 323 |
365 | |
Andere Ausgaben - Alle anzeigen
The Mountain Pass Theorem: Variants, Generalizations and Some Applications Youssef Jabri Keine Leseprobe verfügbar - 2003 |
The Mountain Pass Theorem: Variants, Generalizations and Some Applications Youssef Jabri Keine Leseprobe verfügbar - 2003 |
The Mountain Pass Theorem: Variants, Generalizations and Some Applications Youssef Jabri Keine Leseprobe verfügbar - 2011 |
Häufige Begriffe und Wortgruppen
algorithm Ambrosetti Appl applications Banach space boundary value problems bounded Brézis C¹-functional C¹(X calculus of variations Chapter class C¹ compact Consider continuous function contradiction critical point theory critical set critical value defined definition Denote Diff Dirichlet problem dist eigenvalue Ekeland's principle Ekeland's variational principle elliptic equations elliptic problems exists Ghoussoub Hamiltonian systems Hilbert space implies inequality inf max inf sup linear linking Lipschitz continuous Ljusternik-Schnirelman locally Lipschitz functionals mapping Math metric space minimal minimax Morse Morse index mountain pass point mountain pass theorem neighborhood nonempty Nonlinear Anal nonsmooth nontrivial solutions notion Palais-Smale condition perturbation positive solutions proof Proposition proved PS)c Rabinowitz saddle point satisfies Schechter semilinear elliptic equations sequence un)n Sobolev Sobolev spaces superlinear Suppose symmetric MPT topological variational methods Willem
Beliebte Passagen
Seite 325 - A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann.
Seite 327 - Morse theory for symmetric functionals on the sphere and an application to a bifurcation problem, Nonlinear Analysis TMA Vol.
Seite 327 - V. Benci, A geometrical index for the group Sl and some applications to the study of periodic solutions of ordinary differential equations, Comm. Pure Appl. Math. 34 (1981), 393-432.
Seite 327 - On the Morse indices of sign changing solutions of nonlinear elliptic problems. Math. Z., 233, no.
Verweise auf dieses Buch
Nonsmooth Variational Problems and Their Inequalities: Comparison Principles ... Siegfried Carl,Vy Khoi Le,Dumitru Motreanu Eingeschränkte Leseprobe - 2007 |