Analysis and Topology in Nonlinear Differential Equations
Analysis and Topology in Nonlinear Differential Equations

Author: Djairo G de Figueiredo

Publisher: Springer

Published: 2014-06-16

Total Pages: 465

ISBN-13: 3319042149

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This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

Fixed points and topological degree in nonlinear analysis
Fixed points and topological degree in nonlinear analysis

Author: Jane Cronin

Publisher: American Mathematical Soc.

Published: 1995-01-05

Total Pages: 212

ISBN-13: 0821815113

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The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with ``large'' nonlinearities. Then, after being extended to infinite-dimensional ``function-spaces'', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.

Topological Nonlinear Analysis
Topological Nonlinear Analysis

Author: Michele Matzeu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 542

ISBN-13: 1461225701

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Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.

Topological Nonlinear Analysis II
Topological Nonlinear Analysis II

Author: Michele Matzeu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 609

ISBN-13: 146124126X

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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.

A Topological Introduction to Nonlinear Analysis
A Topological Introduction to Nonlinear Analysis

Author: Robert F. Brown

Publisher: Springer

Published: 2014-11-27

Total Pages: 229

ISBN-13: 3319117947

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This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)

Nonlinear Analysis
Nonlinear Analysis

Author: Themistocles M Rassias

Publisher: World Scientific

Published: 1988-01-01

Total Pages: 571

ISBN-13: 9814513652

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Contents: Fixed Point Theory and Nonlinear Problems (Th Rassias)Global Linearization Iterative Methods and Nonlinear Partial Differential Equations III (M Altman)On Generalized Power Series and Generalized Operational Calculus and Its Application (M Al-Bassam)Multiple Solutions to Parametrized Nonlinear Differential Systems from Nielsen Fixed Point Theory (R Brown)The topology of Ind-Affine Sets (P Cherenack)Almost Approximately Polynomial Functions (P Cholewa)Cohomology Classes and Foliated Manifolds (M Craioveanu & M Puta)Bifurcation and Nonlinear Instability in Applied Mathematics (L Debnath)The Stability of Weakly Additive Functional (H Drljevic)Index Theory for G-Bundle Pairs with Applications to Borsuk-Ulam Type Theorems for G-Sphere Bundles (E Fadell & S Husseini)Nonlinear Approximation and Moment Problem (J S Hwang & G D Lin)Periods in Equicontinuous Topological Dynamical Systems (A Iwanik et al.)Continuation Theorems for Semi-Linear Equations in Banach Spaces: A Survey (J Mawhin & K Rybakowski)On Contractifiable Self-Mappings (P Meyers)Normal Structures and Nonexpansive Mappings in Banach Spaces (J Nelson et al.): Survey on Uniqueness and Classification Theorems for Minimal Surfaces (Th Rassias)Contractive Definitions (B Rhoades)On KY Fan's Theorem and Its Applications (S Singh)Fixed Points of Amenable Semigroups of Differentiable Operators (P Soardi)Research Problems on Nonlinear Equations (Th Rassias) Readership: Mathematicians and applied scientists. Keywords:Nonlinear Analysis;Nonlinear Partial Differential Equations III;Polynomial Functions;Cohomology Classes;Foliated Manifolds;Topological Dynamical Systems;Minimal Surfaces;Differentiable Operators;Nonlinear Equations

Homotopy Analysis Method in Nonlinear Differential Equations
Homotopy Analysis Method in Nonlinear Differential Equations

Author: Shijun Liao

Publisher: Springer Science & Business Media

Published: 2012-06-22

Total Pages: 566

ISBN-13: 3642251323

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"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems
Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 2013-11-19

Total Pages: 465

ISBN-13: 1461493234

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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.

Order Structure and Topological Methods in Nonlinear Partial Differential Equations
Order Structure and Topological Methods in Nonlinear Partial Differential Equations

Author: Yihong Du

Publisher: World Scientific

Published: 2006

Total Pages: 202

ISBN-13: 9812566244

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The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.