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Variational, Topological, and Partial Order Methods with Their Applications

Author : Zhitao Zhang
Publisher : Springer Science & Business Media
Release Date : 2012-09-18
ISBN : 3642307086
Pages : 333 pages
Rating : 4.2/5 (37 Download)

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Download Free Variational, Topological, and Partial Order Methods with Their Applications PDF by Zhitao Zhang Full Book and published by Springer Science & Business Media. This book was released on 2012-09-18 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.

Variational, Topological, and Partial Order Methods with Their Applications

Author : Zhitao Zhang
Publisher : Springer Science & Business Media
Release Date : 2012-09-17
ISBN : 3642307094
Pages : 332 pages
Rating : 4.2/5 (37 Download)

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Download Free Variational, Topological, and Partial Order Methods with Their Applications PDF by Zhitao Zhang Full Book and published by Springer Science & Business Media. This book was released on 2012-09-17 with total page 332 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.

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author : Dumitru Motreanu
Publisher : Springer Science & Business Media
Release Date : 2013-11-19
ISBN : 1461493234
Pages : 459 pages
Rating : 4.1/5 (493 Download)

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Download Free Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems PDF by Dumitru Motreanu Full Book 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.

Variational Methods

Author : Michael Struwe
Publisher : Springer Science & Business Media
Release Date : 2013-04-17
ISBN : 3662032120
Pages : 272 pages
Rating : 4.2/5 (32 Download)

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Download Free Variational Methods PDF by Michael Struwe Full Book and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 272 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.

An Introduction to Minimax Theorems and Their Applications to Differential Equations

Author : Maria do Rosário Grossinho
Publisher : Springer Science & Business Media
Release Date : 2013-06-29
ISBN : 1475733089
Pages : 274 pages
Rating : 4.5/5 (733 Download)

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Download Free An Introduction to Minimax Theorems and Their Applications to Differential Equations PDF by Maria do Rosário Grossinho Full Book and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 274 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.

Nonlinear Functional Analysis and Its Applications

Author : Felix E. Browder
Publisher : American Mathematical Soc.
Release Date : 1986
ISBN : 0821814710
Pages : 540 pages
Rating : 4.1/5 (814 Download)

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Download Free Nonlinear Functional Analysis and Its Applications PDF by Felix E. Browder Full Book and published by American Mathematical Soc.. This book was released on 1986 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Trends in Nonlinear Partial Differential Equations

Author : Patrizia Pucci
Publisher : American Mathematical Soc.
Release Date : 2013
ISBN : 0821898612
Pages : 340 pages
Rating : 4.1/5 (898 Download)

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Download Free Recent Trends in Nonlinear Partial Differential Equations PDF by Patrizia Pucci Full Book and published by American Mathematical Soc.. This book was released on 2013 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes that contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor 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. The workshop program testified to the wide ranging influence of Patrizia Pucci on the field of nonlinear analysis and partial differential equations. In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume. The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolution problems in nonlinear partial differential equations.

Sign-Changing Critical Point Theory

Author : Wenming Zou
Publisher : Springer Science & Business Media
Release Date : 2008-12-15
ISBN : 0387766588
Pages : 310 pages
Rating : 4.7/5 (766 Download)

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Download Free Sign-Changing Critical Point Theory PDF by Wenming Zou Full Book and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 310 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.

Challenges for the 21st Century

Author : L H Y Chen
Publisher : World Scientific
Release Date : 2001-05-08
ISBN : 9814490865
Pages : 528 pages
Rating : 4.4/5 (49 Download)

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Download Free Challenges for the 21st Century PDF by L H Y Chen Full Book and published by World Scientific. This book was released on 2001-05-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Fundamental Sciences: Mathematics and Theoretical Physics provided a forum for reviewing some of the significant developments in mathematics and theoretical physics in the 20th century; for the leading theorists in these fields to expound and discuss their views on new ideas and trends in the basic sciences as the new millennium approached; for increasing public awareness of the importance of basic research in mathematics and theoretical physics; and for promoting a high level of interest in mathematics and theoretical physics among school students and teachers. This was a major conference, with invited lectures by some of the leading experts in various fields of mathematics and theoretical physics. Contents:Mathematics:A Review of Critical Point Theory (K-C Chang)Data Tuning (P Hall)Applied Mathematics Meets Signal Processing (S Mallat)Chromatic Graph Theory (C Thomassen)Three-Dimensional Subgroups and Unitary Representations (D A Vogan, Jr.)Theoretical Physics:The Future of Particle Physics (J D Bjorken)The Mathematics of M-Theory (R Dijkgraaf)Aspects of Anomalies in Field Theory (K Fujikawa)General Relativity and Quantum Mechanics (J B Hartle)Perturbative Quantum Field Theory (G Sterman)and other papers Readership: Researchers in mathematics and theoretical physics. Keywords:Proceedings;Conference;Mathematics;Theoretical Physics;Singapore (Singapore)

Evolution Equations, Semigroups and Functional Analysis

Author : Brunello Terreni
Publisher : Springer Science & Business Media
Release Date : 2002
ISBN : 9783764367916
Pages : 426 pages
Rating : 4.7/5 (911 Download)

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Download Free Evolution Equations, Semigroups and Functional Analysis PDF by Brunello Terreni Full Book and published by Springer Science & Business Media. This book was released on 2002 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition

Author : John Roe
Publisher : CRC Press
Release Date : 1999-01-06
ISBN : 9780582325029
Pages : 222 pages
Rating : 4.5/5 (21 Download)

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Download Free Elliptic Operators, Topology, and Asymptotic Methods, Second Edition PDF by John Roe Full Book and published by CRC Press. This book was released on 1999-01-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.

Fifth International Congress of Chinese Mathematicians

Author : Lizhen Ji
Publisher : American Mathematical Soc.
Release Date : 2012
ISBN : 0821875876
Pages : 999 pages
Rating : 4.1/5 (875 Download)

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Download Free Fifth International Congress of Chinese Mathematicians PDF by Lizhen Ji Full Book and published by American Mathematical Soc.. This book was released on 2012 with total page 999 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.

Elliptic Operators, Topology, and Asymptotic Methods, Second Edition

Author : John Roe
Publisher : CRC Press
Release Date : 2013-12-19
ISBN : 1482247836
Pages : 209 pages
Rating : 4.2/5 (247 Download)

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Download Free Elliptic Operators, Topology, and Asymptotic Methods, Second Edition PDF by John Roe Full Book and published by CRC Press. This book was released on 2013-12-19 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.

Topological Methods in Hydrodynamics

Author : Vladimir I. Arnold
Publisher : Springer Nature
Release Date : 2021-05-12
ISBN : 3030742784
Pages : 455 pages
Rating : 4.0/5 (742 Download)

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Download Free Topological Methods in Hydrodynamics PDF by Vladimir I. Arnold Full Book and published by Springer Nature. This book was released on 2021-05-12 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

Optimization in Science and Engineering

Author : Themistocles M. Rassias
Publisher : Springer
Release Date : 2014-05-29
ISBN : 1493908081
Pages : 610 pages
Rating : 4.3/5 (98 Download)

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Download Free Optimization in Science and Engineering PDF by Themistocles M. Rassias Full Book and published by Springer. This book was released on 2014-05-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science. Topics highlight recent developments and include: Deterministic global optimization Variational inequalities and equilibrium problems Approximation and complexity in numerical optimization Non-smooth optimization Statistical models and data mining Applications of optimization in medicine, energy systems, and complex network analysis This volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.

Partial Differential Equations and the Calculus of Variations

Author : COLOMBINI
Publisher : Springer Science & Business Media
Release Date : 2013-11-11
ISBN : 1461598311
Pages : 1019 pages
Rating : 4.1/5 (598 Download)

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Download Free Partial Differential Equations and the Calculus of Variations PDF by COLOMBINI Full Book and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 1019 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.

Handbook of Differential Equations:Stationary Partial Differential Equations

Author : Michel Chipot
Publisher : Elsevier
Release Date : 2005-08-19
ISBN : 9780080461076
Pages : 624 pages
Rating : 4.1/5 (77 Download)

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Download Free Handbook of Differential Equations:Stationary Partial Differential Equations PDF by Michel Chipot Full Book and published by Elsevier. This book was released on 2005-08-19 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.