Leonid Berezansky's Books

Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

By: Leonid Berezansky,Alexander Domoshnitsky,Roman Koplatadze

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Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

By: Leonid Berezansky,Alexander Domoshnitsky,Roman Koplatadze

Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The control in the mechanical processes leads to mathematical models with second order delay differential equations. Stability and stabilization of second order delay equations are one of the main goals of this book. The book is based on the authors’ results in the last decade. Features: Stability, oscillatory and asymptotic properties of solutions are studied in correlation with each other. The first systematic description of stability methods based on the Bohl-Perron theorem. Simple and explicit exponential stability tests. In this book, various types of functional differential equations are considered: second and higher orders delay differential equations with measurable coefficients and delays, integro-differential equations, neutral equations, and operator equations. Oscillation/nonoscillation, existence of unbounded solutions, instability, special asymptotic behavior, positivity, exponential stability and stabilization of functional differential equations are studied. New methods for the study of exponential stability are proposed. Noted among them inlcude the W-transform (right regularization), a priory estimation of solutions, maximum principles, differential and integral inequalities, matrix inequality method, and reduction to a system of equations. The book can be used by applied mathematicians and as a basis for a course on stability of functional differential equations for graduate students.

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Page Count

488

Publisher

CRC Press

Published Date

ISBN 10

1000048632

ISBN 13

9781000048636

Nonoscillation Theory of Functional Differential Equations with Applications

By: Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky

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Nonoscillation Theory of Functional Differential Equations with Applications

By: Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.

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526

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461434556

ISBN 13

9781461434559

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

By: Leonid Shaikhet

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Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

By: Leonid Shaikhet

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

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Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3319001019

ISBN 13

9783319001012

Ukrainian Dissidents: An Anthology of Texts

By: Oleksii Stus, Dmytro Finberg, Leonid Sinchenko

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Ukrainian Dissidents: An Anthology of Texts

By: Oleksii Stus, Dmytro Finberg, Leonid Sinchenko

This anthology of seminal texts documents the development of the post-war anti-Soviet Ukrainian dissident movement. The collection is designed to introduce, via some crucial primary sources, Western and other non-Ukrainian readers to various forms of Ukrainian opposition to the communist regime. Stories of ideas and personal undertakings are unfolding before the reader in a vivid pulsation of texts that testify for themselves. The anthology gathers contributions from different genres. They range from poetry, public speeches, and samvydav—uncensored, self-published—texts to court speeches. They come from dissidents who were held in jails, special psychiatric hospitals (for not accepting the official ideology), and prison camps. Finally, they include self-reflections by dissidents on their personal experience of opposing the totalitarian system. This variety of contributions creates a multidimensional picture of the Ukrainian dissident movement—a generation of prominent Ukrainian public and cultural figures who, in one way or another, insisted on their freedom of speech and made history by daring to challenge the official ideology and culture. This remarkable book about the struggle for freedom has been compiled by Oleksii Sinchenko, Dmytro Stus, and Leonid Finberg. Scholarly reviewed by Myroslav Marynovych.

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Page Count

412

Publisher

BoD – Books on Demand

Published Date

ISBN 10

3838215516

ISBN 13

9783838215518

Nonoscillation Theory of Functional Differential Equations with Applications

By: Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky

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Nonoscillation Theory of Functional Differential Equations with Applications

By: Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky

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N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

526

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461434556

ISBN 13

9781461434559

Book's by Leonid Berezansky

Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

Nonoscillation Theory of Functional Differential Equations with Applications

Nonoscillation Theory of Functional Differential Equations with Applications

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Ukrainian Dissidents: An Anthology of Texts

Ukrainian Dissidents: An Anthology of Texts

Nonoscillation Theory of Functional Differential Equations with Applications

Nonoscillation Theory of Functional Differential Equations with Applications

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