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Morse Theory Minimax Theory And Their Applications To Nonlinear Differential Equations
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Book Synopsis Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations by : Haim Brézis
Download or read book Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations written by Haim Brézis and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains both survey and creative papers dealing with Morse theory, minimax theory, iteration theory of Maslov-type index and critical minimization problems. The book particularly emphasizes applications to nonlinear differential equations.
Book Synopsis Infinite Dimensional Morse Theory and Multiple Solution Problems by : K.C. Chang
Download or read book Infinite Dimensional Morse Theory and Multiple Solution Problems written by K.C. Chang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Book Synopsis Minimax Methods in Critical Point Theory with Applications to Differential Equations by : Paul H. Rabinowitz
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.
Book Synopsis Infinite Dimensional Morse Theory and Multiple Solution Problems by : K.C. Chang
Download or read book Infinite Dimensional Morse Theory and Multiple Solution Problems written by K.C. Chang and published by Birkhäuser. This book was released on 2011-09-26 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Book Synopsis Perspectives in Nonlinear Partial Differential Equations by : Henri Berestycki
Download or read book Perspectives in Nonlinear Partial Differential Equations written by Henri Berestycki and published by American Mathematical Soc.. This book was released on 2007 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.
Book Synopsis Stable Solutions of Elliptic Partial Differential Equations by : Louis Dupaigne
Download or read book Stable Solutions of Elliptic Partial Differential Equations written by Louis Dupaigne and published by CRC Press. This book was released on 2011-03-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
Book Synopsis Geometry of PDEs and Related Problems by : Xavier Cabré
Download or read book Geometry of PDEs and Related Problems written by Xavier Cabré and published by Springer. This book was released on 2018-10-03 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.
Download or read book Minimax Theorems written by Michel Willem and published by Springer Science & Business Media. This book was released on 1997-02-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for an advanced graduate course in partial differential equations. Presents basic minimax theorems starting from a quantitative deformation lemma; and demonstrates their applications to partial differential equations, particularly in problems dealing with a lack of compactness. Includes some previously unpublished results such as a treatment of the generalized Kadomtsev-Petviashvili equation. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Solvability of Nonlinear Singular Problems for Ordinary Differential Equations by : Irena Rachunkova
Download or read book Solvability of Nonlinear Singular Problems for Ordinary Differential Equations written by Irena Rachunkova and published by Hindawi Publishing Corporation. This book was released on 2009 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mountain Pass Theorem by : Youssef Jabri
Download or read book The Mountain Pass Theorem written by Youssef Jabri and published by Cambridge University Press. This book was released on 2003-09-15 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Functional Analysis And Applications To Differential Equations: Proceedings Of The Second School by : Antonio Ambrosetti
Download or read book Nonlinear Functional Analysis And Applications To Differential Equations: Proceedings Of The Second School written by Antonio Ambrosetti and published by World Scientific. This book was released on 1998-09-02 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced level textbook is devoted to the description of systems which show ordered magnetic phases. A wide selection of topics is covered, including a detailed treatment of the mean-field approximation as the main paradigm for the phenomenological description of phase transitions. The book discusses the properties of low-dimensional systems and uses Green's functions extensively after a useful mathematical introduction. A thorough presentation of the RKKY and related models of indirect exchange is also featured, and a chapter on surface magnetism, rarely found in other textbooks, adds to the uniqueness of this book.For the second edition, three new chapters have been added, namely on magnetic anisotropy, on coherent magnon states and on local moments. Additionally, the chapter on itinerant magnetism has been enlarged by including a section on paramagnons.
Download or read book Minimax Theorems written by Michel Willem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
Book Synopsis Sign-Changing Critical Point Theory by : Wenming Zou
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.
Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot
Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2006-08-08 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics
Author :Zdzislaw Denkowski Publisher :Springer Science & Business Media ISBN 13 :9780306474569 Total Pages :844 pages Book Rating :4.4/5 (745 download)
Book Synopsis An Introduction to Nonlinear Analysis: Applications by : Zdzislaw Denkowski
Download or read book An Introduction to Nonlinear Analysis: Applications written by Zdzislaw Denkowski and published by Springer Science & Business Media. This book was released on 2003-01-31 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.
Author :Maria do Rosário Grossinho Publisher :Springer Science & Business Media ISBN 13 :1475733089 Total Pages :279 pages Book Rating :4.4/5 (757 download)
Book Synopsis An Introduction to Minimax Theorems and Their Applications to Differential Equations by : Maria do Rosário Grossinho
Download or read book An Introduction to Minimax Theorems and Their Applications to Differential Equations written by Maria do Rosário Grossinho and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.
