The Mountain Pass Theorem: Variants, Generalizations and Some Applications

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Mai 2011



This 2003 book presents min-max methods through a study of the different faces of the Mountain Pass Theorem of Ambrosetti and Rabinowitz.


1. Retrospective; Part I. First Steps toward the Mountains: 2. Palais-Smale condition. Definitions and examples; 3. Variational principle; 4. Deformation lemma; Part II. Reaching the Mountain Pass through Easy Climbs: 5. The finite dimensional MPT; 6. The topological MPT; 7. The classical MPT; 8. The multidimensional MPT; Part III. A Deeper Insight in Mountain Topology: 9. The limiting case in the MPT; 10. Palais-Smale condition versus asymptotic behavior; 11. Symmetry and the MPT; 12. The structure of the critical set in the MPT; 13. Weighted Palais-Smale conditions; Part IV. The Landscape Becoming Less Smooth: 14. The semismooth MPT; 15. The nonsmooth MPT; 16. The metric MPT; Part V. Speculating about the Mountain Pass Geometry: 17. The MPT on convex domains; 18. A MPT in order intervals; 19. The linking principle; 20. The intrinsic MPT; 21. Geometrically contrained MPT; Part VI. Technical Climbs: 22. Numerical MPT implementations; 23. Perturbation from symmetry and the MPT; 24. Applying the MPT in bifurcation problems; 25. More climbs; Appendix A. Background material.


Review of the hardback: 'This impressive research monograph provides an excellent basis for an advanced course or a seminar on problems of modern nonlinear analysis.' Zentralblatt MATH
EAN: 9780521827218
ISBN: 0521827213
Untertitel: 'Encyclopedia of Mathematics an'. New. Sprache: Englisch.
Erscheinungsdatum: Mai 2011
Seitenanzahl: 382 Seiten
Format: gebunden
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