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Author : Vito Volterra
Publisher : Unknown
Page : 316 pages
File Size : 41,9 Mb
Release : 1959
Category : Differential equations
ISBN : UOM:39015000507171
Author : Vito Volterra
Publisher : Unknown
Page : 223 pages
File Size : 52,7 Mb
Release : 1944
Category : Electronic
ISBN : OCLC:912240674
Author : V. Lakshmikantham
Publisher : CRC Press
Page : 376 pages
File Size : 53,5 Mb
Release : 1995-03-15
Category : Mathematics
ISBN : 2884490000
This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.
Author : Harendra Singh,Hemen Dutta,Marcelo M. Cavalcanti
Publisher : Springer Nature
Page : 255 pages
File Size : 48,9 Mb
Release : 2021-04-16
Category : Technology & Engineering
ISBN : 9783030655099
This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations
Author : Theodore Allen Burton
Publisher : Elsevier
Page : 369 pages
File Size : 44,6 Mb
Release : 2005-05-21
Category : Mathematics
ISBN : 9780444517869
Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. Smooth transition from ordinary differential equations to integral and functional differential equations Unification of the theories, methods, and applications of ordinary and functional differential equations Large collection of examples of Liapunov functions Description of the history of stability theory leading up to unsolved problems Applications of the resolvent to stability and periodic problems
Author : Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko
Publisher : CRC Press
Page : 582 pages
File Size : 46,5 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 0824703960
A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.
Author : C. Corduneanu
Publisher : CRC Press
Page : 185 pages
File Size : 49,7 Mb
Release : 2002-09-05
Category : Mathematics
ISBN : 9780203166376
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 : Ravi P. Agarwal,Donal O'Regan
Publisher : CRC Press
Page : 344 pages
File Size : 43,8 Mb
Release : 2000-03-09
Category : Mathematics
ISBN : 905699221X
This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.
Author : Griffith Conrad Evans
Publisher : Unknown
Page : 186 pages
File Size : 40,9 Mb
Release : 1964
Category : Functional analysis
ISBN : STANFORD:36105031206571
Author : Praveen Agarwal,Ravi P Agarwal,Michael Ruzhansky
Publisher : CRC Press
Page : 371 pages
File Size : 48,6 Mb
Release : 2020-09-08
Category : Mathematics
ISBN : 9781000078565
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
Author : Marko Kostic
Publisher : Unknown
Page : 0 pages
File Size : 40,9 Mb
Release : 2019-09-19
Category : Electronic
ISBN : 0367377675
The theory of linear Volterra Integro-differental equations has been developing rapidly in the last three decades. This book provides an easy-to-read, concise introduction to the theory of ill-posed abstract Volterra Integro-differential equations. It is accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. Each chapter is further divided into sections and subsections, and contains plenty of examples and open problems.
Author : D.D. Bainov,P.S Simeonov
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 44,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401580342
This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.
Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
Page : 560 pages
File Size : 50,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881598
This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.
Author : Hermann Brunner
Publisher : Cambridge University Press
Page : 620 pages
File Size : 45,9 Mb
Release : 2004-11-15
Category : Mathematics
ISBN : 0521806151
Publisher Description
Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
Page : 556 pages
File Size : 48,5 Mb
Release : 1985-08-21
Category : Mathematics
ISBN : 9780691083629
"This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author"--Publisher description.