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Abstract Volterra Integro-Differential Equations

Author: Marko Kostic

Publisher: CRC Press

Published: 2015-05-06

Total Pages: 480

ISBN-13: 148225431X

The theory of linear Volterra integro-differential 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. A major part of the research is devoted to the study of various types of abstract (multi-term) fracti

Theory of Integro-Differential Equations

Author: V. Lakshmikantham

Publisher: CRC Press

Published: 1995-03-15

Total Pages: 376

ISBN-13: 9782884490009

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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.

Linear and Nonlinear Integral Equations

Author: Abdul-Majid Wazwaz

Publisher: Springer Science & Business Media

Published: 2011-11-24

Total Pages: 639

ISBN-13: 3642214495

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Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.

Nonlinear Integral Equations in Abstract Spaces

Author: Dajun Guo

Publisher: Springer Science & Business Media

Published: 2013-11-22

Total Pages: 350

ISBN-13: 1461312817

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Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.

Volterra Integral and Differential Equations

Author: Burton

Publisher: Academic Press

Published: 1983-11-04

Total Pages: 312

ISBN-13: 0080956734

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Volterra Integral and Differential Equations

Metrical Almost Periodicity and Applications to Integro-Differential Equations

Author: Marko Kostić

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-06-06

Total Pages: 576

ISBN-13: 3111233871

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Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

Author: Marko Kostić

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-05-06

Total Pages: 372

ISBN-13: 3110641259

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This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Recent Studies in Differential Equations

Author: Henry Forster

Publisher:

Published: 2020

Total Pages: 130

ISBN-13: 9781536184297

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"This compilation introduces and studies the class of (asymptotically) Stepanov almost automorphic functions with variable exponents, presenting a few relevant applications of abstract Volterra integro-differential inclusions in Banach spaces. The authors study the existence and regularity of solutions for some nonlinear second order differential equations, showing the existence of mild solutions and giving sufficient conditions ensuring the existence of strict solutions. Sufficient conditions for the oscillation of solutions of neutral impulsive differential equations are also presented. In the penultimate study, the oscillatory behaviour of the solutions of a class of nonlinear first-order neutral differential equations with several delays of one form are studied. In addition, some sufficient conditions for the oscillation of solutions to the first and second-order neutral delay difference equation are presented"--

Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

Author: Marko Kostić

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-05-06

Total Pages: 372

ISBN-13: 3110641852

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Volterra Equations and Applications

Author: C. Corduneanu

Publisher: CRC Press

Published: 2000-01-10

Total Pages: 512

ISBN-13: 1482287420

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This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in th