Linking Methods In Critical Point Theory

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Linking Methods In Critical Point Theory

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Author : Martin Schechter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linking Methods In Critical Point Theory written by Martin Schechter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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

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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15

Sign Changing Critical Point Theory written by Wenming Zou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.

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.

Minimax Systems And Critical Point Theory

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Author : Martin Schechter
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28

Minimax Systems And Critical Point Theory written by Martin Schechter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Mathematics categories.

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

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Author : Kanishka Perera
language : en
Publisher: Cambridge University Press
Release Date : 2013

Topics In Critical Point Theory written by Kanishka Perera and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

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

Critical Point Theory And Its Applications

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Author : Wenming Zou
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10

Critical Point Theory And Its Applications written by Wenming Zou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-10 with Mathematics categories.

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.

Abstract And Applied Analysis

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Author : N. M. Chuong
language : en
Publisher: World Scientific
Release Date : 2004

Abstract And Applied Analysis written by N. M. Chuong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with History categories.

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

The Mountain Pass Theorem

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Author : Youssef Jabri
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15

The Mountain Pass Theorem written by Youssef Jabri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Mathematics categories.

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.

Handbook Of Topological Fixed Point Theory

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Author : Robert F. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-10

Handbook Of Topological Fixed Point Theory written by Robert F. Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-10 with Mathematics categories.

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 Differential Equations And Applications

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Author : Themistocles M. Rassias
language : en
Publisher: Springer Nature
Release Date : 2021-08-20

Nonlinear Analysis Differential Equations And Applications written by Themistocles M. Rassias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-20 with Mathematics categories.

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers–Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg–Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Morse Theoretic Aspects Of P Laplacian Type Operators

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Author : Kanishka Perera
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Morse Theoretic Aspects Of P Laplacian Type Operators written by Kanishka Perera and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Presents a Morse theoretic study of a very general class of homogeneous operators that includes the $p$-Laplacian as a special case. The $p$-Laplacian operator is a quasilinear differential operator that arises in many applications such as non-Newtonian fluid flows. Working with a new sequence of eigenvalues that uses the cohomological index, the authors systematically develop alternative tools such as nonlinear linking and local splitting theories in order to effectively apply Morse theory to quasilinear problems.