Sign Changing Critical Point Theory
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Sign Changing Critical Point Theory
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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Sign Changing Critical Point Theory written by Wenming Zou 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 2008-12-15 with Mathematics categories.
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.
Critical Point Theory And Its Applications
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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
Critical Point Theory And Its Applications written by Wenming Zou 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 2006-09-10 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.
Duality And Perturbation Methods In Critical Point Theory
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Author : Nassif Ghoussoub
language : en
Publisher: Cambridge University Press
Release Date : 1993-08-19
Duality And Perturbation Methods In Critical Point Theory written by Nassif Ghoussoub and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-19 with Mathematics categories.
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.
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.
Recent Trends In Nonlinear Partial Differential Equations Ii
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Author : James Serrin
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Recent Trends In Nonlinear Partial Differential Equations Ii written by James Serrin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This book is the second of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honour of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.
Handbook Of Differential Equations Stationary Partial Differential Equations
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Author : Michel Chipot
language : en
Publisher: Elsevier
Release Date : 2005-08-19
Handbook Of Differential Equations Stationary Partial Differential Equations written by Michel Chipot and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-19 with Mathematics categories.
A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.
Topological Methods Variational Methods And Their Applications Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis
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Author : Haim Brezis
language : en
Publisher: World Scientific
Release Date : 2003-03-13
Topological Methods Variational Methods And Their Applications Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis written by Haim Brezis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-13 with Mathematics categories.
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University.166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Topological Methods Variational Methods And Their Applications
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Author : Haim Brzis
language : en
Publisher: World Scientific
Release Date : 2003
Topological Methods Variational Methods And Their Applications written by Haim Brzis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Variational Methods Open Problems Recent Progress And Numerical Algorithms
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Author : John Neuberger
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Variational Methods Open Problems Recent Progress And Numerical Algorithms written by John Neuberger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.
Progress In Variational Methods
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Author : Chungen Liu
language : en
Publisher: World Scientific
Release Date : 2010
Progress In Variational Methods written by Chungen Liu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.