Volterra Integral and Functional Equations »

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