E-Book Overview
Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more. He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included.
E-Book Content
P1: FCH/FFX
P2: FCH/FFX
0521827213cInd-01
QC: FCH/FFX
CB577/Jabri-v1.cls
T1: FCH June 27, 2003
This page intentionally left blank
20:16
P1: FCH/FFX
P2: FCH/FFX
CB577/Jabri-FM
QC: FCH/FFX
T1: FCH
CB577/Jabri-v1.cls
July 24, 2003
10:15
The Mountain Pass Theorem Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis). This book presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is gently 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: the classical and dual MPT; second-order information from (PS) sequences; symmetry and topological index theory; perturbations from symmetry; convexity; and more. But it also covers other topics covered nowhere else in book form: the nonsmooth 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.
i
P1: FCH/FFX CB577/Jabri-FM
P2: FCH/FFX
QC: FCH/FFX
T1: FCH
CB577/Jabri-v1.cls
July 24, 2003
ii
10:15
P1: FCH/FFX
P2: FCH/FFX
CB577/Jabri-FM
QC: FCH/FFX
T1: FCH
CB577/Jabri-v1.cls
July 24, 2003
10:15
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS FOUNDING EDITOR G.-C. ROTA Editorial Board
R. Doran, P. Flajolet, M. Ismail, T.-Y. Lam, E. Lutwak 95 The Mountain Pass Theorem 40 41 42 43 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
N. White (ed.) Matroid Applications S. Sakai Operator Algebras in Dynamical Systems W. Hodges Basic Model Theory H. Stahl and V. Totik General Orthogonal Polynomials G. Da Prato and J. Zabczyk Stochastic Equations in Infinite Dimensions A. Bj¨orner et al. Oriented Matroids G. Edgar and L. Sucheston Stopping Times and Directed Processes C. Sims Computation with Finitely Presented Groups T. Palmer Banach Algebras and the General Theory of *-Algebras I F. Borceux Handbook of Categorical Algebra I F. Borceux Handbook of Categorical Algebra II F. Borceux Handbook of Categorical Algebra III V. F. Kolchin Random Graphs A. Katok and B. Hasselblatt Introduction to the Modern Theory of Dynamical Systems V. N. Sachkov Combinatorial Methods in Discrete Mathematics V. N. Sachkov