Duality and Perturbation Methods in Critical Point Theory

ISBN-13: 9780521440257 / Angielski / Twarda / 1993 / 280 str.

Nassif Ghoussoub; N. Ghoussoub; B. Bollobas

Opis

Building on min-max methods, Professor Ghoussoub systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole new array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book self-contained.

Recenzje

"...Each chapter ends with some historical notes and comments, which offer a very useful guide through the literature on the subjects mentioned." Maria Letizia Bertotti, Mathematical Reviews

Spis treści

1. Lipschitz and smooth perturbed minimization principles; 2. Linear and plurisubharmonic perturbed minimization principles; 3. The classical min-max theorem; 4. A strong form of the min-max principle; 5. Relaxed boundary conditions in the presence of a dual set; 6. The critical set in the mountain pass theorem; 7. Group actions and multiplicity of critical points; 8. The Palais–Smale condition around a dual set - examples; 9. Morse indices of min-max critical points - the non-degenerate case; 10. Morse indices of min-max critical points - the degenerate case; 11. Morse-type information on Palais–Smale sequences; Appendix; References; Index.