Theory Of Causal Differential Equations

Author : S. Leela,V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 47,5 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9789491216251

Get Book

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS by S. Leela,V. Lakshmikantham Pdf

The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.

Author : S. Leela,Z. Drici,F. A. McRae
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2010
Category : Differential equations
ISBN : 1282749056

Get Book

Theory of Causal Differential Equations by S. Leela,Z. Drici,F. A. McRae Pdf

The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.

Author : V. Lakshmikantham
Publisher : Atlantis Studies in Mathematic
Page : 0 pages
File Size : 52,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9078677325

Get Book

Theory of Causal Differential Equations by V. Lakshmikantham Pdf

The theory of causal differential equations (CDE) includes several types of dynamic systems such as ordinary differential equations, functional differential equations, integro-differential equations (with or without memory), differential equations with anticipation and retardation. This is the first book which describes the theory of CDE as an independent discipline, incorporating the recent general theory of CDE and introducing several new ideas. This book is a timely introduction to the subject in a more generalised frame work. The present monograph collects recent works in this broad area and provides possible extensions to other dynamic systems involving causal operators such as CDE in abstract spaces, CDE with memory, CDE with fractional derivatives and causal set differential equations-giving initial apparatus, for further study in this important branch of nonlinear analysis.

Author : C. Corduneanu
Publisher : CRC Press
Page : 185 pages
File Size : 54,5 Mb
Release : 2002-09-05
Category : Mathematics
ISBN : 9780203166376

Get Book

Functional Equations with Causal Operators by C. Corduneanu Pdf

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau

Author : Andrew Russell Forsyth
Publisher : CUP Archive
Page : 364 pages
File Size : 42,9 Mb
Release : 1959
Category : Differential equations
ISBN : 8210379456XXX

Get Book

Theory of Differential Equations by Andrew Russell Forsyth Pdf

Author : Andrew Russell Forsyth
Publisher : Unknown
Page : 364 pages
File Size : 41,6 Mb
Release : 1890
Category : Differential equations
ISBN : UCAL:B4649563

Get Book

Theory of Differential Equations ... by Andrew Russell Forsyth Pdf

Author : Lieberstein
Publisher : Academic Press
Page : 282 pages
File Size : 41,9 Mb
Release : 1972-11-07
Category : Computers
ISBN : 9780080956022

Get Book

Theory of Partial Differential Equations by Lieberstein Pdf

Theory of Partial Differential Equations

Author : Anatoly A. Martynyuk
Publisher : Springer
Page : 198 pages
File Size : 44,5 Mb
Release : 2019-04-02
Category : Mathematics
ISBN : 9783030076443

Get Book

Qualitative Analysis of Set-Valued Differential Equations by Anatoly A. Martynyuk Pdf

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.

Author : Angela Slavova
Publisher : Springer Nature
Page : 457 pages
File Size : 41,5 Mb
Release : 2023-03-17
Category : Mathematics
ISBN : 9783031214844

Get Book

New Trends in the Applications of Differential Equations in Sciences by Angela Slavova Pdf

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.

Author : Raymond M. Redheffer,Dan Port
Publisher : Jones & Bartlett Learning
Page : 744 pages
File Size : 45,8 Mb
Release : 1991
Category : Mathematics
ISBN : 0867202009

Get Book

Differential Equations by Raymond M. Redheffer,Dan Port Pdf

Author : L Dresner
Publisher : CRC Press
Page : 242 pages
File Size : 53,6 Mb
Release : 1998-01-01
Category : Science
ISBN : 1420050788

Get Book

Applications of Lie's Theory of Ordinary and Partial Differential Equations by L Dresner Pdf

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Author : Randal H. Cole
Publisher : Unknown
Page : 304 pages
File Size : 43,5 Mb
Release : 1968
Category : Mathematics
ISBN : STANFORD:36105031262905

Get Book

Theory of Ordinary Differential Equations by Randal H. Cole Pdf

Author : Sigeru Mizohata
Publisher : CUP Archive
Page : 518 pages
File Size : 41,6 Mb
Release : 1973-08-02
Category : Mathematics
ISBN : 0521087279

Get Book

The Theory of Partial Differential Equations by Sigeru Mizohata Pdf

Fourier series and fourier transforms; Distributions; Elliptic equations (fundamental theory); Initial value problems (cauchy problems); Evolution equations; Hyperbolic equations; Semi-linear hyperbolic equations; Green's functions and spectra.

Author : Constantin Corduneanu,Yizeng Li,Mehran Mahdavi
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 50,5 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781119189473

Get Book

Functional Differential Equations by Constantin Corduneanu,Yizeng Li,Mehran Mahdavi Pdf

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 presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

Author : George F. Carrier,Carl E. Pearson
Publisher : Academic Press
Page : 333 pages
File Size : 51,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483259161

Get Book

Partial Differential Equations by George F. Carrier,Carl E. Pearson Pdf

Partial Differential Equations: Theory and Technique provides formal definitions, notational conventions, and a systematic discussion of partial differential equations. The text emphasizes the acquisition of practical technique in the use of partial differential equations. The book contains discussions on classical second-order equations of diffusion, wave motion, first-order linear and quasi-linear equations, and potential theory. Certain chapters elaborate Green's functions, eigenvalue problems, practical approximation techniques, perturbations (regular and singular), difference equations, and numerical methods. Students of mathematics will find the book very useful.