Linking Methods In Critical Point Theory

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Linking Methods in Critical Point Theory

Martin Schechter
Linking Methods in Critical Point Theory Book PDF

Author : Martin Schechter
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215967

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Linking Methods in Critical Point Theory by Martin Schechter Pdf

As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the Trans-Canada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on ...

Sign-Changing Critical Point Theory

Wenming Zou
Sign Changing Critical Point Theory Book PDF

Author : Wenming Zou
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 40,8 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387766584

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Sign-Changing Critical Point Theory by Wenming Zou Pdf

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

Martin Schechter
Critical Point Theory Book PDF

Author : Martin Schechter
Publisher : Springer Nature
Page : 347 pages
File Size : 49,5 Mb
Release : 2020-05-30
Category : Mathematics
ISBN : 9783030456030

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Critical Point Theory by Martin Schechter Pdf

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.

Topics in Critical Point Theory

Kanishka Perera,Martin Schechter
Topics in Critical Point Theory Book PDF

Author : Kanishka Perera,Martin Schechter
Publisher : Cambridge University Press
Page : 171 pages
File Size : 42,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9781107029668

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Topics in Critical Point Theory by Kanishka Perera,Martin Schechter Pdf

Provides an introduction to critical point theory and shows how it solves many difficult problems.

Critical Point Theory and Its Applications

Wenming Zou,Martin Schechter
Critical Point Theory and Its Applications Book PDF

Author : Wenming Zou,Martin Schechter
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 47,6 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780387329680

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Critical Point Theory and Its Applications by Wenming Zou,Martin Schechter Pdf

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.

Minimax Systems and Critical Point Theory

Martin Schechter
Minimax Systems and Critical Point Theory Book PDF

Author : Martin Schechter
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 54,7 Mb
Release : 2009-05-28
Category : Mathematics
ISBN : 9780817649029

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Minimax Systems and Critical Point Theory by Martin Schechter Pdf

This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.

Handbook of Topological Fixed Point Theory

Robert F. Brown
Handbook of Topological Fixed Point Theory Book PDF

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 40,6 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 1402032218

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Handbook of Topological Fixed Point Theory by Robert F. Brown Pdf

This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Nonlinear Analysis - Theory and Methods

Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš
Nonlinear Analysis Theory and Methods Book PDF

Author : Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš
Publisher : Springer
Page : 577 pages
File Size : 40,8 Mb
Release : 2019-02-26
Category : Mathematics
ISBN : 9783030034306

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Nonlinear Analysis - Theory and Methods by Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš Pdf

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

An Introduction to Nonlinear Analysis

Martin Schechter
An Introduction to Nonlinear Analysis Book PDF

Author : Martin Schechter
Publisher : Cambridge University Press
Page : 380 pages
File Size : 50,8 Mb
Release : 2004
Category : Mathematics
ISBN : 0521843979

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An Introduction to Nonlinear Analysis by Martin Schechter Pdf

The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.

Nonlinear Analysis and Variational Problems

Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan
Nonlinear Analysis and Variational Problems Book PDF

Author : Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 53,6 Mb
Release : 2009-10-20
Category : Business & Economics
ISBN : 9781441901583

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Nonlinear Analysis and Variational Problems by Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan Pdf

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Topological Methods, Variational Methods and Their Applications

Haim Br‚zis
Topological Methods Variational Methods and Their Applications Book PDF

Author : Haim Br‚zis
Publisher : World Scientific
Page : 300 pages
File Size : 54,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812382627

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Topological Methods, Variational Methods and Their Applications by Haim Br‚zis Pdf

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.

Minimax Methods in Critical Point Theory with Applications to Differential Equations

Paul H. Rabinowitz,Conference Board of the Mathematical Sciences
Minimax Methods in Critical Point Theory with Applications to Differential Equations Book PDF

Author : Paul H. Rabinowitz,Conference Board of the Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 49,7 Mb
Release : 1986-07-01
Category : Mathematics
ISBN : 9780821807156

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Minimax Methods in Critical Point Theory with Applications to Differential Equations by Paul H. Rabinowitz,Conference Board of the Mathematical Sciences Pdf

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.

Challenges For The 21st Century, Procs Of The Intl Conf On Fundamental Sciences: Mathematics And Theoretical Physics

Louis Hsiao Yun Chen,Judith Packer Jesudason,Choy Heng Lai,Choo Hiap Oh,Kok Khoo Phua,Eng-chye Tan
Challenges For The 21st Century Procs Of The Intl Conf On Fundamental Sciences Mathematics And Theoretical Physics Book PDF

Author : Louis Hsiao Yun Chen,Judith Packer Jesudason,Choy Heng Lai,Choo Hiap Oh,Kok Khoo Phua,Eng-chye Tan
Publisher : World Scientific
Page : 528 pages
File Size : 47,9 Mb
Release : 2001-05-08
Category : Science
ISBN : 9789814490863

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Challenges For The 21st Century, Procs Of The Intl Conf On Fundamental Sciences: Mathematics And Theoretical Physics by Louis Hsiao Yun Chen,Judith Packer Jesudason,Choy Heng Lai,Choo Hiap Oh,Kok Khoo Phua,Eng-chye Tan Pdf

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.

Topological Methods, Variational Methods and Their Applications

H Brezis,K C Chang,S J Li,P Rabinowitz
Topological Methods Variational Methods and Their Applications Book PDF

Author : H Brezis,K C Chang,S J Li,P Rabinowitz
Publisher : World Scientific
Page : 300 pages
File Size : 51,6 Mb
Release : 2003-03-13
Category : Mathematics
ISBN : 9789814486767

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Topological Methods, Variational Methods and Their Applications by H Brezis,K C Chang,S J Li,P Rabinowitz Pdf

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

Topics in Nonlinear Functional Analysis

L. Nirenberg
Topics in Nonlinear Functional Analysis Book PDF

Author : L. Nirenberg
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 42,8 Mb
Release : 1974
Category : Mathematics
ISBN : 0821883461

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Topics in Nonlinear Functional Analysis by L. Nirenberg Pdf

Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.