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  3. Volterra Integral and Functional Equations
  • Cited by 564
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
1990
Online ISBN:
9780511662805
DOI:
https://doi.org/10.1017/CBO9780511662805
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
Series:
Encyclopedia of Mathematics and its Applications (34)
Information

Book description

The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations. The book is divided into three parts. The first considers linear theory and the second deals with quasilinear equations and existence problems for nonlinear equations, giving some general asymptotic results. Part III is devoted to frequency domain methods in the study of nonlinear equations. The entire text analyses n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalizations to infinite-dimensional spaces. The book is generally self-contained and assumes only a basic knowledge of analysis. The many exercises illustrate the development of the theory and its applications, making this book accessible to researchers in all areas of integral and differential equations.

Reviews

"...an excellent encyclopedia of results on the theory of Volterra integral equations." Mathematical Reviews

"Efforts have been made to cover aspects of analysis needed but not easily found elsewhere...and care is given to including an extensive table of symbols and their meaning; it is nicely produced." The Mathematical Association of America

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