Vicentiu D. Radulescu's Books

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Monotonicity, Analytic, and Variational Methods

By: Vicentiu D. Radulescu,Vicenţiu D. Rădulescu

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Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Monotonicity, Analytic, and Variational Methods

By: Vicentiu D. Radulescu,Vicenţiu D. Rădulescu

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

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Page Count

205

Publisher

Hindawi Publishing Corporation

Published Date

ISBN 10

9774540395

ISBN 13

9789774540394

Partial Differential Equations with Variable Exponents

Variational Methods and Qualitative Analysis

By: Vicentiu D. Radulescu,Dusan D. Repovs

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Partial Differential Equations with Variable Exponents

Variational Methods and Qualitative Analysis

By: Vicentiu D. Radulescu,Dusan D. Repovs

Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational

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Page Count

321

Publisher

CRC Press

Published Date

ISBN 10

1498703445

ISBN 13

9781498703444

Problems in Real Analysis

Advanced Calculus on the Real Axis

By: Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu

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Problems in Real Analysis

Advanced Calculus on the Real Axis

By: Teodora-Liliana Radulescu,Vicentiu D. Radulescu,Titu Andreescu

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

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Page Count

462

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387773797

ISBN 13

9780387773797

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

By: Dumitru Motreanu,Vicentiu D. Radulescu

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Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

By: Dumitru Motreanu,Vicentiu D. Radulescu

This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.

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384

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475769210

ISBN 13

9781475769210

Variational Methods for Nonlocal Fractional Problems

By: Giovanni Molica Bisci,Vicentiu D. Radulescu,Raffaella Servadei

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Variational Methods for Nonlocal Fractional Problems

By: Giovanni Molica Bisci,Vicentiu D. Radulescu,Raffaella Servadei

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

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Page Count

401

Publisher

Cambridge University Press

Published Date

ISBN 10

1316571696

ISBN 13

9781316571699

Variational Methods for Nonlocal Fractional Problems

By: Giovanni Molica Bisci,Vicentiu D. Radulescu,Raffaella Servadei

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Variational Methods for Nonlocal Fractional Problems

By: Giovanni Molica Bisci,Vicentiu D. Radulescu,Raffaella Servadei

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Page Count

401

Publisher

Cambridge University Press

Published Date

ISBN 10

1316571696

ISBN 13

9781316571699

Book's by Vicentiu D. Radulescu

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Partial Differential Equations with Variable Exponents

Partial Differential Equations with Variable Exponents

Problems in Real Analysis

Problems in Real Analysis

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems

Variational Methods for Nonlocal Fractional Problems

Variational Methods for Nonlocal Fractional Problems

Variational Methods for Nonlocal Fractional Problems

Variational Methods for Nonlocal Fractional Problems

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