Duality And Perturbation Methods In Critical Point Theory PDF Download
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Author | : Nassif Ghoussoub |
Publisher | : Cambridge University Press |
Total Pages | : 358 |
Release | : 1993-08-19 |
Genre | : Mathematics |
ISBN | : 9780521440257 |
Download Duality and Perturbation Methods in Critical Point Theory Book in PDF, ePub and Kindle
The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole 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 reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.
Author | : Martin Schechter |
Publisher | : Springer Science & Business Media |
Total Pages | : 305 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146121596X |
Download Linking Methods in Critical Point Theory Book in PDF, ePub and Kindle
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 | : Martin Schechter |
Publisher | : Springer Nature |
Total Pages | : 347 |
Release | : 2020-05-30 |
Genre | : Mathematics |
ISBN | : 303045603X |
Download Critical Point Theory Book in PDF, ePub and Kindle
This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author’s own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book’s main subject: applications to problems in mathematics and physics. These include topics such as Schrödinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.
Author | : Kanishka Perera |
Publisher | : Cambridge University Press |
Total Pages | : 171 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 110702966X |
Download Topics in Critical Point Theory Book in PDF, ePub and Kindle
Provides an introduction to critical point theory and shows how it solves many difficult problems.
Author | : Wenming Zou |
Publisher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 2008-12-15 |
Genre | : Mathematics |
ISBN | : 0387766588 |
Download Sign-Changing Critical Point Theory Book in PDF, ePub and Kindle
Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs. This book is intended for advanced graduate students and researchers involved in sign-changing critical point theory, PDEs, global analysis, and nonlinear functional analysis.
Author | : Martin Schechter |
Publisher | : Springer Science & Business Media |
Total Pages | : 239 |
Release | : 2009-05-28 |
Genre | : Mathematics |
ISBN | : 0817649026 |
Download Minimax Systems and Critical Point Theory Book in PDF, ePub and Kindle
This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.
Author | : Jean Mawhin |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2013-04-17 |
Genre | : Science |
ISBN | : 1475720610 |
Download Critical Point Theory and Hamiltonian Systems Book in PDF, ePub and Kindle
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 | : Wenming Zou |
Publisher | : Springer Science & Business Media |
Total Pages | : 323 |
Release | : 2006-09-10 |
Genre | : Mathematics |
ISBN | : 0387329684 |
Download Critical Point Theory and Its Applications Book in PDF, ePub and Kindle
This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.
Author | : |
Publisher | : |
Total Pages | : 224 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download Canadian Journal of Mathematics Book in PDF, ePub and Kindle
Author | : Nikolaos S. Papageorgiou |
Publisher | : Springer |
Total Pages | : 577 |
Release | : 2019-02-26 |
Genre | : Mathematics |
ISBN | : 3030034305 |
Download Nonlinear Analysis - Theory and Methods Book in PDF, ePub and Kindle
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.