Critical Point Theory And Hamiltonian Systems

Author : Jean Mawhin
Publisher : Springer Science & Business Media
ISBN 13 : 1475720610
Total Pages : 292 pages
Book Rating : 4.17/5 ( download)

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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

Author : Wenming Zou
Publisher : Springer Science & Business Media
ISBN 13 : 0387329684
Total Pages : 323 pages
Book Rating : 4.80/5 ( download)

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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.

Author : Martin Schechter
Publisher : Springer Nature
ISBN 13 : 303045603X
Total Pages : 347 pages
Book Rating : 4.30/5 ( download)

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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.

Author : Wenming Zou
Publisher : Springer Science & Business Media
ISBN 13 : 0387766588
Total Pages : 288 pages
Book Rating : 4.84/5 ( download)

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Download or read book Sign-Changing Critical Point Theory written by Wenming Zou and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9780387512815
Total Pages : 169 pages
Book Rating : 4.10/5 ( download)

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Download or read book Pfahlgründungen written by Dimitrios Kolymbas and published by . This book was released on 1989 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Marco Mazzucchelli
Publisher : Springer Science & Business Media
ISBN 13 : 3034801637
Total Pages : 188 pages
Book Rating : 4.38/5 ( download)

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Download or read book Critical Point Theory for Lagrangian Systems written by Marco Mazzucchelli and published by Springer Science & Business Media. This book was released on 2011-11-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kenneth Meyer
Publisher : Springer Science & Business Media
ISBN 13 : 0387097244
Total Pages : 404 pages
Book Rating : 4.44/5 ( download)

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Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth Meyer and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Paul H. Rabinowitz
Publisher : American Mathematical Soc.
ISBN 13 : 0821889109
Total Pages : 110 pages
Book Rating : 4.07/5 ( download)

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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 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nassif Ghoussoub
Publisher : Cambridge University Press
ISBN 13 : 9780521440257
Total Pages : 358 pages
Book Rating : 4.54/5 ( download)

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Download or read book Duality and Perturbation Methods in Critical Point Theory written by Nassif Ghoussoub and published by Cambridge University Press. This book was released on 1993-08-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kenneth R. Meyer
Publisher : Springer
ISBN 13 : 3319536915
Total Pages : 384 pages
Book Rating : 4.10/5 ( download)

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Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)