The Mountain Pass Theorem: Variants, Generalizations and Some Applications

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.