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theory of integro-differential equations, lakshmikantham [pdf]

Theory of Integro Differential Equations by V. Lakshmikantham and M. Rama Mohana Rao

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Theory of Integro Differential Equations written by V. Lakshmikantham and M. Rama Mohana Rao cover the following topics.

  • 1. Basic theory
    1.0 Introduction
    1.1 Local and Global Existence
    1.2 Integro differential Inequalities
    1.3 Existence of Extermal Solutions
    1.4 Comparison Results
    1.5 Convergence of Successive Approximations
    1.6 Continuous Dependence
    1.7 Linear Variation of Parameters
    1.8 Nonlinear Variation of Parameters
    1.9 Monotone Iterative Technique
    1.10 Interval Analytic Method
    1.11 Notes and Comments

  • 2. Linear Analysis
    2.0 Introduction
    2.1 Basic Properties of Linear Systems
    2.2 Stability of Linear Convolution Systems
    2.3 tability Criteria for General Linear Systems
    2.4 Stability by Method of Reduction
    2.5 Stability in Variation
    2.6 Lipschitz Stability
    2.7 Asympotic Equivalence
    2.8 Ultimate Behaviour of Solutions
    2.9 Difference Equations
    2.10 Impulsive Integro differential Systems
    2.11 Periodic Solutions
    2.12 Notes and Comments

  • 3. Lyapunov Stability
    3.0 Introduction
    3.1 Method of Lyapunov Functionals
    3.2 Equations with Unbounded Delay
    3.3 Perturbed Systems
    3.4 Method of Lyapunov Functions
    3.5 Lyapunov Functions on Product Spaces
    3.6 Impulsive Integro Differential Equations
    3.7 Impulsive Integro Differential Equations(continued)
    3.8 Notes and Comments

  • 4. Equations in Abstract Spaces
    4.0 Intoduction
    4.1 Existence and uniqueness
    4.2 Existence of Maximal and Minimal Solutions
    4.3 Well Posedness of Linear Equations
    4.4 Semigroups and Resolved Operators
    4.5 Evolution Operators and Resolvents
    4.6 Asymtotic Behaviour and Perturbations
    4.7 Stability of Solutions
    4.8 Notes and Comments

  • 5.Applications
    5.0 Intoduction
    5.1 Biological Population
    5.2 Grazing Systems
    5.3 Wave Propagation
    5.4 Nuclear Reactors
    5.5 Viscoelasticity
    5.6 Large Scale Systems
    5.7 Notes and Comments

  • References

  • Index

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