Linking Methods In Critical Point Theory PDF Download
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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 | : 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 | : Paul H. Rabinowitz |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 1986-07-01 |
Genre | : Mathematics |
ISBN | : 0821807153 |
Download Minimax Methods in Critical Point Theory with Applications to Differential Equations Book in PDF, ePub and Kindle
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 | : 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 | : 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 | : 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 | : |
Publisher | : Academic Press |
Total Pages | : 405 |
Release | : 2014-05-14 |
Genre | : Mathematics |
ISBN | : 0080873456 |
Download Critical Point Theory in Global Analysis and Differential Topology Book in PDF, ePub and Kindle
Critical Point Theory in Global Analysis and Differential Topology
Author | : N. M. Chuong |
Publisher | : World Scientific |
Total Pages | : 579 |
Release | : 2004 |
Genre | : History |
ISBN | : 981238944X |
Download Abstract and Applied Analysis Book in PDF, ePub and Kindle
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences