Critical Point Theory And Hamiltonian Systems
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Critical Point Theory And Hamiltonian Systems
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Author : Jean Mawhin
language : en
Publisher:
Release Date : 2014-01-15
Critical Point Theory And Hamiltonian Systems written by Jean Mawhin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Critical Point Theory And Hamiltonian Systems
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Author : Jean Mawhin
language : en
Publisher: Springer
Release Date : 1989-02-08
Critical Point Theory And Hamiltonian Systems written by Jean Mawhin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-08 with Science categories.
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
Critical Point Theory And Its Applications
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Author : Wenming Zou
language : en
Publisher: Springer
Release Date : 2006-06-13
Critical Point Theory And Its Applications written by Wenming Zou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-13 with Mathematics categories.
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.
Critical Point Theory
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Author : Martin Schechter
language : en
Publisher: Springer Nature
Release Date : 2020-05-30
Critical Point Theory written by Martin Schechter and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-30 with Mathematics categories.
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.
Critical Point Theory For Lagrangian Systems
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Author : Marco Mazzucchelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-16
Critical Point Theory For Lagrangian Systems written by Marco Mazzucchelli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-16 with Science categories.
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.
Handbook Of Dynamical Systems
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Author : B. Hasselblatt
language : en
Publisher: Elsevier
Release Date : 2002-08-20
Handbook Of Dynamical Systems written by B. Hasselblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-20 with Mathematics categories.
Volumes 1A and 1B.These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys.The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics.Volume 1B will appear 2005.
Handbook Of Differential Equations Ordinary Differential Equations
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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2005-09-02
Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-02 with Mathematics categories.
This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience. . Six chapters covering a variety of problems in ordinary differential equations. . Both, pure mathematical research and real word applications are reflected. Written by leading researchers in the area.
An Alternative Approach To Critical Point Theory And Its Applications To Hamiltonian Systems
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Author : Leiping Yu
language : en
Publisher:
Release Date : 1998
An Alternative Approach To Critical Point Theory And Its Applications To Hamiltonian Systems written by Leiping Yu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Dynamical Systems
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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2025-06-23
Dynamical Systems written by René Lozi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-23 with Mathematics categories.
This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA. The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for control systems, and chaotic dynamics in remote sensing for crop modeling. It also highlights the role of chaos theory in the development of memristors following Leon Chua’s 1971 discovery, leading to advances in nonlinear dynamics, hyperchaos, and memristor-based systems. The chapters further examine how chaos theory addresses modern challenges such as modeling COVID-19 spread using SEIR models and optimizing mobile network design, demonstrating the wide-reaching impact of chaotic systems in real-world applications. This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications. This book includes a revised introduction and a new chapter. The remaining chapters were originally published in Journal of Difference Equations and Applications.
Control And Boundary Analysis
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Author : John Cagnol
language : en
Publisher: CRC Press
Release Date : 2005-03-04
Control And Boundary Analysis written by John Cagnol and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-04 with Mathematics categories.
This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving bou