Springer, 2012. — 535 p. — ISBN: 1461434548. 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...
Marcel Dekker, 2004. — 371 p. This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential...
Hindawi Publishing, 2007. — 325 p. The book covers many topics in the theory of functional differential equations: key questions of the general theory, boundary value problems (both linear and nonlinear), control problems (with both classic and impulse control), stability problems, calculus of variations problems, computer-assisted techniques for studying the problems mentioned....
New York: Chapman and Hall/CRC, 2020. — 615 p. 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...
Brno: Masaryk University, 2007. — 74 p. Faculty of Science. Notation Definitions and Quoted Statements General Linear Boundary Value Problem Statement of the Problem Existence and Uniqueness Theorems Linear System with a Small Parameter Linear System with Deviating Arguments I Linear System with a Deviating Argument and a Small Parameter Linear System with More Deviating...
Cambridge: CUP, 2004. - 612p.
This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. It guides the reader from the ''basics'' to the current state-of-the-art level...
Academic Press, 1986. — 337 p. In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation...
Wiley, 2016. — 365 p. — (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts). — ISBN10: 1119189470. — ISBN13: 978-1119189473 Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications...
Atlantis Press, 2014. — 311 p. — (Atlantis Studies in Differential Equations 03). — ISBN: 978-94-6239-090-4. Stability of Neutral Functional Differential Equations In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations. The main...
Springer-Verlag New York 2013. — (Applied Mathematical Sciences 184). — 289 pp. — ISBN: 978-1-4614-6991-9 (Print) 978-1-4614-6992-6 (Online).
This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major...
New York: Springer, 1993. — 458 p. The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and...
Boca Raton: CRC Press, 1982. — 352 p. This book contains twenty four papers, presented at the conference on Volterra and Functional Differential Equations held in Virginia in 1981, on various topics, including Liapunov stability, Volterra equations, integral equations, and functional differential equations. Preface Contributors Conference Participants A Survey of Some Problems...
World Scientific, 1995. - 306 pages. ISBN: 9810224052.
Functional differential equations have received attention since the 1920s. Within that development, boundary value problems have played a prominent role both in the theory and applications dating back to the 1960s. This text attempts to present some of the more recent developments from a cross-section of views on boundary...
Springer, 1999. — 176 pages. — ISBN: 978-9048152117 Beginning with the works of N.N.Krasovskii, which clarified the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the...
Amsterdam: Springer, 1992. — 245 p. This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems)....
New York: Springer, 2014. - 160p.
This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world...
Boca Raton: CRC Press, 2017. — 277 p. The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by...
Berlin: de Gruyter, 2009. — 240 p. This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equationsis under rapid development. After a presentation of the...
Springer, 1996. — 440 p. Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical...
М.: Институт компьютерных исследований, 2002. — 385 с. Дается систематическое изложение основ теории линейного абстрактного функционально-дифференциального уравнения. Эта теория позволяет рассматривать с единой точки зрения многочисленные классы уравнений, изучавшихся ранее вне связи друг с другом, в частности, уравнений с сингулярностями, с импульсными воздействиями,...
Учебное пособие. — Москва: Российский университет дружбы народов (РУДН), 2008. — 243 с. В учебном пособии изучаются квазилинейные и линейные параболические и эллиптические функционально-дифференциальные уравнения, содержащие преобразования пространственных переменных неизвестной функции в ограниченной пространственной области. Излагаются актуальные вопросы, возникающие в...
Современная математика. Фундаментальные направления. Том 30 (2008). С. 3–173.
О разрешимости и оценках решений ФДУ параболического типа в пространствах Соболева.
О гладких решениях функционально-дифференциальных уравнений. Условия согласования.
Корректная разрешимость уравнений гиперболического типа с последействием в гильбертовом пространстве.
Описание характеристических...
Almaty: КазНУ, 2019. — 192 p. Some theoretical foundations of oscillations of delay equations are expounded in the textbook: oscillations of delay equations, oscillations of difference equations. The tasks for independent work with solving of concrete examples, brief theory and solution algorithms of the problems, term tasks on sections of oscillations of delay and difference...
М.: Регулярная и хаотическая динамика, 2004. — 256 с. Объектом исследования в данной монографии являются функционально-дифференциальные уравнения, описывающие различные процессы с последствием. В книге излагаются конструкции i-гладкого анализа функционалов применительно к теории функционально-дифференциальных уравнений, приводятся численные алгоритмы решения таких систем и...
Диссертация на соискание ученой степени кандидата физико-математических наук : 01.01.02 – Дифференциальные уравнения. — Российский государственный педагогический университет им. А. И. Герцена. — Санкт-Петербург, 2001. — 111 с. Научный руководитель: д.ф.-м.н., проф. В.Д. Будаев. Научный консультант: д.ф.-м.н., проф. В.Ф. Зайцев. В диссертационной работе рассматривается класс...
Статья. — Современная математика. Фундаментальные направления. — Том 4. — 2003. — с. 5-120. Статья посвящена интересному классу функционально-дифференциальных уравнений (ФДУ), которые названы смешанными (СДУ). Оказалось, что, несмотря на естественность этого класса с позиций общей теории ФДУ, он до сих пор систематически не исследовался. Причина, по-видимому, состоит в том, что...
Перевод с английского С.Н. Шиманова. — Под редакцией А.Д. Мышкиса. — М.: Мир, 1984. — 421 с. Теория функционально-дифференциальных уравнений — важный раздел современной математики, который находит применение в сложных системах автоматического управления, моделях экономической динамики, экологических биологических систем. Автор — известный американский математик, крупный...
Комментарии