Analysis And Topology In Nonlinear Differential Equations
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Analysis and Topology in Nonlinear Differential Equations
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.
A Topological Introduction to Nonlinear Analysis
Author: Robert F. Brown
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
Nonlinear analysis is a remarkable mixture of topology, analysis and applied mathematics. Mathematicians have good reason to become acquainted with this important, rapidly developing subject. But it is a BIG subject. You can feel it: just hold Eberhard Zeidler's Nonlinear Functional Analysis and Its Applications I: Fixed Point Theorems [Z} in your hand. It's heavy, as a 900 page book must be. Yet this is no encyclopedia; the preface accurately describes the " ... very careful selection of material ... " it contains. And what you are holding is only Part I of a five-part work. So how do you get started learning nonlinear analysis? Zeidler's book has a first page, and some people are quite comfortable beginning right there. For an alternative, the bibliography in [Z], which is 42 pages long, contains exposition as well as research results: monographs that explain portions of the subject to a variety of audiences. In particular, [D} covers much of the material of Zeidler's book. What makes this book different? The answer is in three parts: this book is (i) topological (ii) goal-oriented and (iii) a model of its subject.
Nonlinear Analysis - Theory and Methods
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.