Quasilinear Elliptic Equations with Degenerations and Singularities (de Gruyter Nonlinear Analysis and Applications)

"The book is very well written and will be a valuable source for specialists in differential equations, functional analysis, operator theory, and mathematical physics, as well as for non-specialists who want to get an idea of this fascinating field of contemporary nonlinear analysis. The authors have achieved a double goal. On the one hand, they provide a self-contained account which describes the state-of-the-art of nonlinear elliptic equations with degenerations and singularities; on the other, their book will certainly stimulate further research in this field. The reviewer regards the second aspect as at least as important as the first one: in fact, in his opinion a book should open a new field, rather than close it." __Zentralblatt für Mathematik__

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Editor-in-Chief
Jürgen Appell, Würzburg, Germany

Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Alain Bensoussan, Richardson, Texas, USA
Avner Friedman, Columbus, Ohio, USA
Umberto Mosco, Worcester, Massachusetts, USA
Louis Nirenberg, New York, USA
Alfonso Vignoli, Rome, Italy

Editorial Board
Manuel del Pino, Santiago, Chile
Mikio Kato, Nagano, Japan
Wojciech Kryszewski, Toru?, Poland
Simeon Reich, Haifa, Israel

Please submit book proposals to Jürgen Appell.

Titles in planning include

Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018)
Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)
Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-ChiefJürgen Appell, Würzburg, Germany Honorary and Advisory EditorsCatherine Bandle, Basel, SwitzerlandAlain Bensoussan, Richardson, Texas, USAAvner Friedman, Columbus, Ohio, USAUmberto Mosco, Worcester, Massachusetts, USA Editorial BoardManuel del Pino, Bath, UK, and Santiago, ChileMikio Kato, Nagano, JapanWojciech Kryszewski, Toruń, PolandVicenţiu D. Rădulescu, Kraków, PolandSimeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020)Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021) Content: Frontmatter -- List of symbols, theorems, definitions, assumptions, examples -- Chapter 0 Introduction -- Chapter 1 Preliminaries -- Chapter 2 Solvability of nonlinear boundary value problems -- Chapter 3 The degenerated p-Laplacian on a bounded domain -- Chapter 4 The p-Laplacian in RN -- Bibliography -- Index This text presents modern methods and techniques for solving boundary value problems for nonlinear elliptic operators. Focus is upon existence and bifurcation results in appropriate Sobolev spaces. Pavel Drábek, Alois Kufner, Francesco Nicolosi. Includes Bibliographical References (p. [209]-213) And Index.