Volterra Integral and Functional Equations

This book looks at the theories of Volterra integral and functional equations.

G. Gripenberg (Author), S. O. Londen (Author), O. Staffans (Author)

9780521103060, Cambridge University Press

Paperback / softback, published 19 March 2009

724 pages
23.4 x 15.6 x 3.7 cm, 1 kg

"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

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.

Preface
List of symbols
1. Introduction and overview
Part I. Linear Theory: 2. Linear convolution integral equations
3. Linear integrodifferential convolution equations
4. Equations in weighted spaces
5. Completely monotone kernels
6. Nonintegrable kernels with integrable resolvents
7. Unbounded and unstable solutions
8. Volterra equations as semigroups
9. Linear nonconvolution equations
10. Linear nonconvolution equations with measure kernels
Part II. General Nonlinear Theory: 11. Perturbed linear equations
12. Existence of solutions of nonlinear equations
13. Continuous dependence, differentiability and uniqueness
14. Lyapunov techniques
15. General asymptotics
Part III. Frequency Domain and Monotonicity Techniques: 16. Convolution kernels of positive type
17. Frequency domain methods: basic results
18. Frequency domain methods: additional results
19. Combined Lyapunov and frequency domain methods
20. Monotonicity methods
Bibliography
Index.

Subject Areas: Functional analysis & transforms [PBKF]