Nonlinear Problems with Lack of Compactness

Nonlinear Problems with Lack of Compactness PDF

Author: Giovanni Molica Bisci

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-02-08

Total Pages: 290

ISBN-13: 3110652013

DOWNLOAD EBOOK →

This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.

Concentration Compactness

Concentration Compactness PDF

Author: Kyril Tintarev

Publisher: Imperial College Press

Published: 2007

Total Pages: 279

ISBN-13: 1860947972

DOWNLOAD EBOOK →

Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.

Yamabe-type Equations on Complete, Noncompact Manifolds

Yamabe-type Equations on Complete, Noncompact Manifolds PDF

Author: Paolo Mastrolia

Publisher: Birkhäuser

Published: 2012-08-01

Total Pages: 260

ISBN-13: 9783034803779

DOWNLOAD EBOOK →

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.

Weak Convergence Methods For Semilinear Elliptic Equations

Weak Convergence Methods For Semilinear Elliptic Equations PDF

Author: Jan Chabrowski

Publisher: World Scientific

Published: 1999-10-19

Total Pages: 247

ISBN-13: 9814494267

DOWNLOAD EBOOK →

This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrödinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais-Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration-compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik-Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions.

Calculus of Variations and Partial Differential Equations

Calculus of Variations and Partial Differential Equations PDF

Author: Luigi Ambrosio

Publisher: Springer Science & Business Media

Published: 2000-01-24

Total Pages: 364

ISBN-13: 9783540648031

DOWNLOAD EBOOK →

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Nonlinear partial differential equations in differential geometry

Nonlinear partial differential equations in differential geometry PDF

Author: Robert Hardt

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 356

ISBN-13: 9780821804315

DOWNLOAD EBOOK →

This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.

Progress in Nonlinear Analysis

Progress in Nonlinear Analysis PDF

Author: Gongqing Zhang

Publisher: World Scientific

Published: 2000

Total Pages: 472

ISBN-13: 9789810243296

DOWNLOAD EBOOK →

The real world is complicated, as a result of which most mathematical models arising from mechanics, physics, chemistry and biology are nonlinear. Based on the efforts of scientists in the 20th century, especially in the last three decades, topological, variational, geometrical and other methods have developed rapidly in nonlinear analysis, which made direct studies of nonlinear models possible in many cases, and provided global information on nonlinear problems which was not available by the traditional linearization method. This volume reflects that rapid development in many areas of nonlinear analysis.

Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping

Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping PDF

Author: Igor Chueshov

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 200

ISBN-13: 0821841874

DOWNLOAD EBOOK →

The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which--in addition to nonlinear dissipation-- have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theoryto nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras PDF

Author: Aref Jeribi

Publisher: CRC Press

Published: 2015-08-14

Total Pages: 369

ISBN-13: 1498733891

DOWNLOAD EBOOK →

Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices w

Lanterna Rally - Theme by Grace Themes