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Topological Methods Variational Methods And Their Applications
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Book Synopsis Topological Methods, Variational Methods and Their Applications by : Haim Brzis
Download or read book Topological Methods, Variational Methods and Their Applications written by Haim Brzis and published by World Scientific. This book was released on 2003 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Methods, Variational Methods and Their Applications by : Haim Brzis
Download or read book Topological Methods, Variational Methods and Their Applications written by Haim Brzis and published by World Scientific. This book was released on 2003 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Methods, Variational Methods and Their Applications by : H Brezis
Download or read book Topological Methods, Variational Methods and Their Applications written by H Brezis and published by World Scientific. This book was released on 2003-03-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:The Underlying Geometry of the Fixed Centers Problems (A Albouy)Critical Equations for the Polyharmonic Operator (T Bartsch)Heat Method in Nonlinear Elliptic Equations (K-C Chang)Boundary Blow-Up Solutions and Their Applications (Y H Du)Fixed Points of Increasing Operator (F Y Li)Collinear Central Configurations in Celestial Mechanics (Y M Long & S Z Sun)Remarks on a Priori Estimates for Superlinear Elliptic Problems (M Ramos)A Semilinear Schrödinger Equation with Magnetic Field (A Szulkin)Sign Changing Solutions of Superlinear Schrödinger Equations (T Weth)Computational Theory and Methods for Finding Multiple Critical Points (J X Zhou)and other papers Readership: Researchers and graduate students in nonlinear differential equations, nonlinear functional analysis, dynamical systems, mathematical physics etc. Keywords:Variational Mthods;Topological Methods;Hamiltonian Systems;Nonlinear Schrödinger Equation;Dynamic System
Book Synopsis Variational and Topological Methods in the Study of Nonlinear Phenomena by : V. Benci
Download or read book Variational and Topological Methods in the Study of Nonlinear Phenomena written by V. Benci and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. A broad range of topics is covered, including: * concentration phenomena in pdes * variational methods with applications to pdes and physics * periodic solutions of odes * computational aspects in topological methods * mathematical models in biology Though well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors: M. Clapp, M. Del Pino, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Séré, E. Schwartzman, P. Sintzoff, R. Turner , M. Willem.
Book Synopsis Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems by : Dumitru Motreanu
Download or read book Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Book Synopsis Variational, Topological, and Partial Order Methods with Their Applications by : Zhitao Zhang
Download or read book Variational, Topological, and Partial Order Methods with Their Applications written by Zhitao Zhang and published by Springer Science & Business Media. This book was released on 2012-09-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Book Synopsis Topological and Variational Methods for Nonlinear Boundary Value Problems by : Pavel Drabek
Download or read book Topological and Variational Methods for Nonlinear Boundary Value Problems written by Pavel Drabek and published by CRC Press. This book was released on 1997-04-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the rapidly developing area of nonlinear theory of differential equations, many important results have been obtained by the use of nonlinear functional analysis based on topological and variational methods. The survey papers presented in this volume represent the current state of the art in the subject. The methods outlined in this book can be used to obtain new results concerning the existence, uniqueness, multiplicity, and bifurcation of the solutions of nonlinear boundary value problems for ordinary and partial differential equations. The contributions to this volume are from well known mathematicians, and every paper contained in this book can serve both as a source of reference for researchers working in differential equations and as a starting point for those wishing to pursue research in this direction. With research reports in the field typically scattered in many papers within various journals, this book provides the reader with recent results in an accessible form.
Book Synopsis Variational Methods for Discontinuous Structures by : Gianni Dal Maso
Download or read book Variational Methods for Discontinuous Structures written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2002 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the International Workshop "Variational Methods For Discontinuous Structures", held at Villa Erba Antica (Cernobbio) on the Lago di Como, July 4-6, 2001. The workshop was jointly organized by the Dipartimento di Matematica Francesco Brioschi of Milano Politecnico and the International School for Advanced Studies (SISSA) of Trieste. In past years the calculus of variations faced mainly the study of continuous structures, particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities. In many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, variational description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes. In most cases theoretical and numerical analysis of these models were provided. Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport problems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework. This volume contains contributions by 12 of the 16 speakers invited to deliver lectures in the workshop. Most of the contributions present original results in fields which are rapidly evolving at present.
Book Synopsis Progress in Variational Methods by : Chungen Liu
Download or read book Progress in Variational Methods written by Chungen Liu and published by World Scientific. This book was released on 2010-09-07 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Nonlinear Analysis II by : Michele Matzeu
Download or read book Topological Nonlinear Analysis II written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Book Synopsis Topological Methods in Galois Representation Theory by : Victor P. Snaith
Download or read book Topological Methods in Galois Representation Theory written by Victor P. Snaith and published by Courier Corporation. This book was released on 2013-12-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph on Galois representation theory by a renowned algebraist covers abelian and nonabelian cohomology of groups, characteristic classes of forms and algebras, explicit Brauer induction theory, more. 1989 edition.
Book Synopsis Progress in Variational Methods by : Chungen Liu
Download or read book Progress in Variational Methods written by Chungen Liu and published by World Scientific. This book was released on 2010-09-07 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:On 2-Tori Having a Pole (V Bangert)Turing Patterns and Standing Waves in Fitzhugh-Nagumo Type Systems (C-N Chen & S-Y Kung)Remarks on Mean Value Properties (Y Y Li & L Nguyen)Brake Orbits in Bounded Convex Symmetric Domains (C Liu & D Zhang)Recent Progress on Closed Geodesics in Some Compact Simply Connected Manifolds (Y Long)Topological Bifurcation Theory: Old and New (J Mawhin)Exponential Growth Rate of Paths and Its Connection with Dynamics (Z Xia & P Zhang)Rabinowitz's Theorems Revisited (W Zou)and other papers Readership: Graduates student and young scholars interested in variational methods. Keywords:Variational Methods;Periodical Solutions;Homoclinics and Heteroclinics of Hamiltonian Systems;Closed Geodesic Flows;Critical Point Theory;Harmonic Maps
Book Synopsis Variational Methods in Shape Optimization Problems by : Dorin Bucur
Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Book Synopsis Variational and Monotonicity Methods in Nonsmooth Analysis by : Nicuşor Costea
Download or read book Variational and Monotonicity Methods in Nonsmooth Analysis written by Nicuşor Costea and published by Springer Nature. This book was released on 2021-09-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern and comprehensive presentation of a wide variety of problems arising in nonlinear analysis, game theory, engineering, mathematical physics and contact mechanics. It includes recent achievements and puts them into the context of the existing literature. The volume is organized in four parts. Part I contains fundamental mathematical results concerning convex and locally Lipschits functions. Together with the Appendices, this foundational part establishes the self-contained character of the text. As the title suggests, in the following sections, both variational and topological methods are developed based on critical and fixed point results for nonsmooth functions. The authors employ these methods to handle the exemplary problems from game theory and engineering that are investigated in Part II, respectively Part III. Part IV is devoted to applications in contact mechanics. The book will be of interest to PhD students and researchers in applied mathematics as well as specialists working in nonsmooth analysis and engineering.
Book Synopsis Applications of the Topological Derivative Method by : Antonio André Novotny
Download or read book Applications of the Topological Derivative Method written by Antonio André Novotny and published by Springer. This book was released on 2018-12-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
