Book:V. Lakshmikantham/Dynamic Systems on Measure Chains

V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan: Dynamic Systems on Measure Chains

Contents

Preface

Chapter 1

1.0 Introduction

1.1 Measure chains and time scales

1.2 Differentiation

1.3 Mean value theorem and consequences

1.4 Integral and antiderivative

1.5 Notes

Chapter 2

2.0 Introduction

2.1 Local existence and uniqueness

2.2 Dynamic inequalities

2.3 Existence of extremal solutions

2.4 Comparison results

2.5 Linear variation of parameters

2.6 Continuous dependence

2.7 Nonlinear variation of parameters

2.8 Global existence and stability

2.9 Notes

Chapter 3

3.0 Introduction

3.1 Comparison theorems

3.2 Stability criteria

3.3 A technique in stability theory

3.4 Stability of conditionally invariant sets

3.5 Stability in terms of two measures

3.6 Vector Lyapunov functions and practical stability

3.7 Notes

Chapter 4

4.0 Introduction

4.1 Monotone iterative technique

4.2 Method of quasilinearization

4.3 Monotone flows and stationary points

4.4 Invariant manifolds

4.5 Practical stability of large-scale uncertain dynamical systems

4.6 Boundary value problems

4.7 Sturmian theory

4.8 Convexity of solutions relative to the initial data

4.9 Invariance principle

4.10 Notes

References

Subject Index