Differential and Integral Inequalities Theory and Applications, Vol. 1 Ordinary Differential Equations

V. LAKSHILIIKANTHAM and S. LEELA
{Jnioersity of Rho& Islmiii
Kiiqstow, Rliotlc Island

Contents
PREFACE
ORDINARY DIFFERENTIAL EQUATIONS
Introduction
Existence and Continuation of Solutions
Scalar Differential Inequalities
Maximal and Minimal Solutions
Comparison Theorems
Finite Systems of Differential Inequalities
Minimax Solutions
Further Comparison Theorems
Infinite Systems of Differential Inequalities
Integral Inequalities Reducible to Differential Inequalities
Differential Inequalities in the Sense of Caratheodory
Notes
Introduction
Global Existence
Uniqueness
Convergence of Successive Approximations
Chaplygin’s Method
Dependence on Initial Conditions and Parameters
Variation of Constants
Upper and Lower Bounds
Componentwise Bounds
Asymptotic Equilibrium
Asynlptotic Equivalence
A Topological Principle
Applications of Topological Principle
Stability Criteria
Asymptotic Behavior
Periodic and Almost Periodic Systems
Chapter 3. 3.0.
Introduction
Basic Comparison Theorems
Definitions
Stability
Asymptotic Stability
Stability of Perturbed Systems
Convcrse Theorems
Stability by the First Approximation
Total Stability
Integral Stability
I,”-S ta hi I i ty
Partial Stability
Stabilit) of Differential Inequalities
Boundcdness and Lagrange Stability
Eventual Stability
Asymptotic Behavior
Relative Stability
Stability with Respect to a Manifold
.-\lmost Periodic Systems
Uniqueness and Estimates
Continuous Dependence and the Method of Averaging
Notes
Introduction
Main Comparison Theorem
Asymptotic Stability
Instability
Conditional Stability and Boundedness
Converse Theorcms
Stability in Tube-like Domain
Stability of Asymptotically Self-Inwriant Sets
Stability of Conditionally Invariant Sets
Existence and Stability of Stationary Points
Notes
VOLTERRA INTEGRAL EQUATIONS
Chapter 5. 5.0.
Introduction
Integral Inequaiitics
Local and Global Existence
Comparison Theorems
Approximate Solutions, Bounds, and Uniqueness
Asymptotic Behavior
Perturbed Integral Equations
Admissibility and Asymptotic Behavior
Integrodifferential Inequalities
Notes
Bibliography
AUTHOR INDEX
SUBJECT INDEX


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