The Mountain Pass Theorem PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Mountain Pass Theorem PDF full book. Access full book title The Mountain Pass Theorem by Youssef Jabri. Download full books in PDF and EPUB format.
Author: Youssef Jabri
Publisher:
ISBN: 9780511071133
Category : Critical point theory (Mathematical analysis)
Languages : en
Pages : 369
Get Book Here
Book Description
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 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 non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants.
Author: Youssef Jabri
Publisher:
ISBN: 9780511071133
Category : Critical point theory (Mathematical analysis)
Languages : en
Pages : 369
Get Book Here
Book Description
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 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 non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants.
Author: Youssef Jabri
Publisher: Cambridge University Press
ISBN: 9780521827218
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Paul H. Rabinowitz
Publisher: American Mathematical Soc.
ISBN: 0821807153
Category : Mathematics
Languages : en
Pages : 110
Get Book Here
Book Description
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
Author: Michel Willem
Publisher: Springer Science & Business Media
ISBN: 1461241464
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
Book Description
Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
Author: Martin Schechter
Publisher: Springer Science & Business Media
ISBN: 9780817640958
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on ...
Author: Youssef Jabri
Publisher: Cambridge University Press
ISBN: 9781139440813
Category : Mathematics
Languages : en
Pages : 390
Get Book Here
Book Description
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.
Author: Nikolaos S. Papageorgiou
Publisher: Springer
ISBN: 3030034305
Category : Mathematics
Languages : en
Pages : 586
Get Book Here
Book Description
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
Author: Jean Mawhin
Publisher: Springer Science & Business Media
ISBN: 1475720610
Category : Science
Languages : en
Pages : 292
Get Book Here
Book Description
FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN
Author: Liviu Nicolaescu
Publisher: Springer Science & Business Media
ISBN: 146141105X
Category : Mathematics
Languages : en
Pages : 366
Get Book Here
Book Description
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
Author: Marston Morse
Publisher: American Mathematical Soc.
ISBN: 0821810189
Category : Mathematics
Languages : en
Pages : 384
Get Book Here
Book Description
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
