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Volterra Integral and Functional Equations


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: March 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521103060

£ 92.99

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About the Authors
  • 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.

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    Product details

    • Date Published: March 2009
    • format: Paperback
    • isbn: 9780521103060
    • length: 724 pages
    • dimensions: 234 x 156 x 37 mm
    • weight: 1kg
    • availability: Available
  • Table of Contents

    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

  • Authors

    G. Gripenberg, Helsinki University of Technology

    S. O. Londen, Helsinki University of Technology

    O. Staffans, Helsinki University of Technology

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