Download or read book Critical Point Theory and Its Applications written by Wenming Zou and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Minimax Methods in Critical Point Theory with Applications to Differential Equations written by Paul H. Rabinowitz and published by American Mathematical Soc.. This book was released on 1986-07-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Critical Point Theory and Submanifold Geometry written by Richard S. Palais and published by Springer. This book was released on 2006-11-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Critical Point Theory and Hamiltonian Systems written by Jean Mawhin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Critical Point Theory written by Martin Schechter and published by Springer Nature. This book was released on 2020-05-30 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linking Methods in Critical Point Theory written by Martin Schechter and published by Springer Science & Business Media. This book was released on 1999-07-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ...
Download or read book The Critical Point written by C Domb and published by CRC Press. This book was released on 1996-02-20 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between liquids and gases engaged the attention of a number of distinguished scientists in the mid 19th Century. In a definitive paper published in 1869, Thomas Andrews described experiments he performed on carbon dioxide and from which he concluded that a critical temperature exists below which liquids and gases are distinct phase
Download or read book Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems written by Leszek Gasinski and published by CRC Press. This book was released on 2004-07-27 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.
Download or read book Critical Point Theory in Global Analysis and Differential Topology written by and published by Academic Press. This book was released on 2014-05-14 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical Point Theory in Global Analysis and Differential Topology
Download or read book Duality and Perturbation Methods in Critical Point Theory written by N. Ghoussoub and published by Cambridge University Press. This book was released on 2008-08-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Cortex and the Critical Point written by John M. Beggs and published by MIT Press. This book was released on 2022-08-30 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: How the cerebral cortex operates near a critical phase transition point for optimum performance. Individual neurons have limited computational powers, but when they work together, it is almost like magic. Firing synchronously and then breaking off to improvise by themselves, they can be paradoxically both independent and interdependent. This happens near the critical point: when neurons are poised between a phase where activity is damped and a phase where it is amplified, where information processing is optimized, and complex emergent activity patterns arise. The claim that neurons in the cortex work best when they operate near the critical point is known as the criticality hypothesis. In this book John Beggs—one of the pioneers of this hypothesis—offers an introduction to the critical point and its relevance to the brain. Drawing on recent experimental evidence, Beggs first explains the main ideas underlying the criticality hypotheses and emergent phenomena. He then discusses the critical point and its two main consequences—first, scale-free properties that confer optimum information processing; and second, universality, or the idea that complex emergent phenomena, like that seen near the critical point, can be explained by relatively simple models that are applicable across species and scale. Finally, Beggs considers future directions for the field, including research on homeostatic regulation, quasicriticality, and the expansion of the cortex and intelligence. An appendix provides technical material; many chapters include exercises that use freely available code and data sets.
Download or read book A Primer to the Theory of Critical Phenomena written by Jurgen M. Honig and published by Elsevier. This book was released on 2018-02-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Primer to the Theory of Critical Phenomena provides scientists in academia and industry, as well as graduate students in physics, chemistry, and geochemistry with the scientific fundamentals of critical phenomena and phase transitions. The book helps readers broaden their understanding of a field that has developed tremendously over the last forty years. The book also makes a great resource for graduate level instructors at universities. - Provides a thorough and accessible treatment of the fundamentals of critical phenomena - Offers an in-depth exposition on renormalization and field theory techniques - Includes experimental observations of critical effects - Includes live examples illustrating the applications of the theoretical material
Download or read book Cirque Du Freak A Living Nightmare written by Darren Shan and published by Little, Brown Books for Young Readers. This book was released on 2008-08-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Master of Horror comes the first gripping book in the twelve book New York Times bestselling Saga of Darren Shan. Start the tale from the beginning in the book that inspired the feature film The Vampire's Assistant and petrified devoted fans worldwide. A young boy named Darren Shan and his best friend, Steve, get tickets to the Cirque Du Freak, a wonderfully gothic freak show featuring weird, frightening half human/half animals who interact terrifyingly with the audience. In the midst of the excitement, true terror raises its head when Steve recognizes that one of the performers-- Mr. Crepsley-- is a vampire! Stever remains after the show finishes to confront the vampire-- but his motives are surprising! In the shadows of a crumbling theater, a horrified Darren eavesdrops on his friend and the vampire, and is witness to a monstrous, disturbing plea. As if by destiny, Darren is pulled to Mr. Crepsley and what follows is his horrifying descent into the dark and bloody world of vampires. This is the beginning of Darren's story.
Download or read book Stratified Morse Theory written by Mark Goresky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.
Download or read book Topological Methods in Differential Equations and Inclusions written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.
Download or read book The Idea of a Critical Theory written by Raymond Geuss and published by Cambridge University Press. This book was released on 1981-10-30 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this series is to help make contemporary European philosophy intelligible to a wider audience in the English-speaking world, and to suggest its interest and importance in particular to those trained in analytical philosophy.
Download or read book Symmetry and Perturbation Theory written by Simonetta Abenda and published by World Scientific. This book was released on 2002 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth conference on OC Supersymmetry and Perturbation TheoryOCO (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and SchrAdinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna); On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava); Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Yu N Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii); Inverse Problems for SL (2) Lattices (V B Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M Rodr guez-Olmos & M E Sousa Dias); A Spectral Sequences Approach to Normal Forms (J A Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nuclear Motion in Molecules (V G Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinear science."
