Volterra Integral and Functional Equations [Hardcover]

This book looks at the theories of Volterra integral and functional equations.This book looks at Volterra integral and functional equations, and 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 generally self-contained and assumes only a basic knowledge of analysis.This book looks at Volterra integral and functional equations, and 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 generally self-contained and assumes only a basic knowledge of analysis.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 analyzes n-dimensional rather than scalar equations, giving greater generality and wider applicability and facilitating generalizations to infinite-dimensional spaces.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. Exils*