Critical Point Theory And Hamiltonian Systems PDF Download
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| 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 | : 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 | : 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 | : Dimitrios Kolymbas |
| Publisher | : |
| Total Pages | : 169 |
| Release | : 1989 |
| Genre | : Gründung (Bauwesen) |
| ISBN | : 9780387512815 |
Download Pfahlgründungen Book in PDF, ePub and Kindle
| Author | : Marco Mazzucchelli |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 196 |
| Release | : 2011-11-16 |
| Genre | : Science |
| ISBN | : 3034801637 |
Download Critical Point Theory for Lagrangian Systems Book in PDF, ePub and Kindle
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange’s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.
| 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 | : Alberto Abbondandolo |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2001-03-15 |
| Genre | : Mathematics |
| ISBN | : 1482285746 |
Download Morse Theory for Hamiltonian Systems Book in PDF, ePub and Kindle
This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals. Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new proof of the equivalence between the Hamiltonian and the Lagrangian index. It also examines the superquadratic Hamiltonian, proving the existence of periodic orbits that do not necessarily satisfy the Rabinowitz condition, studies asymptotically linear systems in detail, and discusses the Arnold conjectures about the number of fixed points of Hamiltonian diffeomorphisms of compact symplectic manifolds. In six succinct chapters, the author provides a self-contained treatment with full proofs. The purely abstract functional aspects have been clearly separated from the applications to Hamiltonian systems, so many of the results can be applied in and other areas of current research, such as wave equations, Chern-Simon functionals, and Lorentzian geometry. Morse Theory for Hamiltonian Systems not only offers clear, well-written prose and a unified account of results and techniques, but it also stimulates curiosity by leading readers into the fascinating world of symplectic topology.
| Author | : Kenneth Meyer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 0387097244 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.
| Author | : Kenneth R. Meyer |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 3319536915 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
