Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations PDF

Author: V. Lakshmikantham

Publisher: CRC Press

Published: 2003-02-27

Total Pages: 328

ISBN-13: 1482288273

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A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combin

Nonsmooth Variational Problems and Their Inequalities

Nonsmooth Variational Problems and Their Inequalities PDF

Author: Siegfried Carl

Publisher: Springer Science & Business Media

Published: 2007-06-07

Total Pages: 404

ISBN-13: 038746252X

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This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

Nonlinear Analysis

Nonlinear Analysis PDF

Author: Leszek Gasinski

Publisher: CRC Press

Published: 2005-07-27

Total Pages: 984

ISBN-13: 1420035045

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Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. Thi

Theory of Fuzzy Differential Equations and Inclusions

Theory of Fuzzy Differential Equations and Inclusions PDF

Author: V. Lakshmikantham

Publisher: CRC Press

Published: 2004-11-23

Total Pages: 192

ISBN-13: 9780203011386

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Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems PDF

Author: Leszek Gasinski

Publisher: CRC Press

Published: 2004-07-27

Total Pages: 790

ISBN-13: 1420035037

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Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of problems.

Topological Degree Theory and Applications

Topological Degree Theory and Applications PDF

Author: Yeol Je Cho

Publisher: CRC Press

Published: 2006-03-27

Total Pages: 228

ISBN-13: 1420011480

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Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its ap

New Trends in the Applications of Differential Equations in Sciences

New Trends in the Applications of Differential Equations in Sciences PDF

Author: Angela Slavova

Publisher: Springer Nature

Published: 2023-03-17

Total Pages: 457

ISBN-13: 3031214846

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This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis. In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations. The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

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