Linking Methods in Critical Point Theory
Linking Methods in Critical Point Theory

Author: Martin Schechter

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 146121596X

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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 ...

Linking Methods in Critical Point Theory
Linking Methods in Critical Point Theory

Author: Martin Schechter

Publisher: Springer Science & Business Media

Published: 1999-07-01

Total Pages: 320

ISBN-13: 9780817640958

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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 ...

Minimax Methods in Critical Point Theory with Applications to Differential Equations
Minimax Methods in Critical Point Theory with Applications to Differential Equations

Author: Paul H. Rabinowitz

Publisher: American Mathematical Soc.

Published: 1986-07-01

Total Pages: 110

ISBN-13: 0821807153

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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.

Sign-Changing Critical Point Theory
Sign-Changing Critical Point Theory

Author: Wenming Zou

Publisher: Springer Science & Business Media

Published: 2008-12-15

Total Pages: 288

ISBN-13: 0387766588

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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
Critical Point Theory

Author: Martin Schechter

Publisher: Springer Nature

Published: 2020-05-30

Total Pages: 347

ISBN-13: 303045603X

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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.

Critical Point Theory and Its Applications
Critical Point Theory and Its Applications

Author: Wenming Zou

Publisher: Springer Science & Business Media

Published: 2006-09-10

Total Pages: 323

ISBN-13: 0387329684

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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
Minimax Systems and Critical Point Theory

Author: Martin Schechter

Publisher: Springer Science & Business Media

Published: 2009-05-28

Total Pages: 239

ISBN-13: 0817649026

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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.

Topics in Critical Point Theory
Topics in Critical Point Theory

Author: Kanishka Perera

Publisher: Cambridge University Press

Published: 2013

Total Pages: 171

ISBN-13: 110702966X

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

Abstract and Applied Analysis
Abstract and Applied Analysis

Author: N. M. Chuong

Publisher: World Scientific

Published: 2004

Total Pages: 579

ISBN-13: 981238944X

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This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences