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Tables of Contents for Method of Variation of Parameters for Dynamic Systems
Chapter/Section Title
Page #
Page Count
Preface
vii
Ordinary Differential Equations
1
64
Introduction
1
1
Linear Variation of Parameters
2
2
Nonlinear Variation of Parameters
4
15
VPF in Terms of Lyapunov-Like Functions
19
1
Boundary Value Problems
20
4
Monotone Iterative Technique
24
3
Exponential Dichotomy
27
7
Sensitivity Analysis
34
4
Existence of Almost Periodic Solutions
38
5
Stability and Asymptotic Behavior
43
10
Controllability
53
5
Variational Comparison Result
58
6
Notes
64
1
Integrodifferential Equations
65
38
Introduction
65
1
Linear Variation of Parameters
65
11
Nonlinear Variation of Parameters
76
5
Monotone Iterative Technique
81
5
Stability Criteria
86
9
Controllability
95
5
Notes
100
3
Differential Equations with Delay
103
38
Introduction
103
1
Linear Variation of Parameters
103
8
Nonlinear Variation of Parameters
111
7
VPF in Terms of Lyapunov-Like Functions
118
4
Asymptotically Self-Invariant Sets
122
2
Asymptotic Equivalence
124
10
Generalized Comparison Principle
134
6
Notes
140
1
Difference Equations
141
34
Introduction
141
1
Linear Variation of Parameters
141
8
Nonlinear Variation of Parameters
149
7
Periodic Solutions
156
3
Boundary Value Problems
159
4
Stability Properties
163
8
Numerical Methods
171
3
Notes
174
1
Abstract Differential Equations
175
28
Introduction
175
1
Notation and Preliminaries
175
2
Linear Variation of Parameters
177
1
Nonlinear Variation of Parameters
178
10
Growth Properties of Solutions
188
7
Stability Behavior
195
6
Notes
201
2
Impulsive Differential Equations
203
30
Introduction
203
1
Preliminaries
203
2
Linear Variation of Parameters
205
7
Nonlinear Variation of Parameters
212
4
Generalized Comparison Principle
216
4
Periodic Boundary Value Problem
220
3
Complete Controllability
223
4
Stability Criteria
227
4
Notes
231
2
Stochastic Differential Equations
233
32
Introduction
233
1
Preliminaries
233
3
Linear Variation of Parameters
236
2
Nonlinear Variation of Parameters
238
10
VPF in Terms of Lyapunov-Like Functions
248
4
Ito-Type System of Equations
252
4
Boundedness of Solutions
256
7
Notes
263
2
Miscellaneous Equations
265
38
Introduction
265
1
Equations with Piecewise Constant Delay
265
11
Complex Differential Equations
276
6
Hyperbolic Differential Equations
282
6
Operator Equations
288
2
Dynamic Systems on Measure Chains
290
11
Notes
301
2
Bibliography
303
12
Index
315