Volterra Integral and Functional Equations
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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.
