| Preface to the Second Edition |
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v | |
| Preface |
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vii | |
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1 | (66) |
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1 | (1) |
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1.1 Gronwall--Type Inequalities |
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2 | (10) |
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1.2 Wendorff--Type Inequalities |
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12 | (4) |
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1.3 Bihari--Type Inequalities |
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16 | (8) |
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1.4 Multivariate Inequalities |
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24 | (2) |
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1.5 Differential Inequalities |
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26 | (5) |
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1.6 Integral Inequalities |
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31 | (4) |
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1.7 General Integral Inequalities |
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35 | (3) |
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1.8 Integro--Differential Inequalities |
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38 | (8) |
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1.9 Difference Inequalities |
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46 | (6) |
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1.10 Interval-Valued Integral Inequalities |
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52 | (4) |
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1.11 Inequalities for Piecewise Continuous Functions |
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56 | (5) |
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1.12 Reaction-Diffusion Inequalities |
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61 | (4) |
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65 | (2) |
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2 Variation of Parameters and Monotone Technique |
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67 | (68) |
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67 | (1) |
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2.1 Nonlinear Variation of Parameters |
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68 | (5) |
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2.2 Estimates of Solutions |
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73 | (10) |
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2.3 Global Existence and Terminal Value Problems |
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83 | (6) |
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89 | (4) |
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2.5 Method of Upper and Lower Solutions |
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93 | (3) |
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2.6 Monotone Iterative Technique |
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96 | (4) |
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2.7 Method of Mixed Monotony |
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100 | (3) |
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2.8 Method of Lower and Upper Solutions and Interval Analysis |
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103 | (3) |
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2.9 Integro-Differential Equations |
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106 | (10) |
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2.10 Stability in Variation |
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116 | (7) |
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2.11 Difference Equations |
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123 | (10) |
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133 | (2) |
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3 Stability of Motion in Terms of Two Measures |
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135 | (66) |
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135 | (1) |
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3.1 Basic Comparison Results |
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136 | (4) |
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3.2 Stability Concepts in Terms of Two Measures |
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140 | (3) |
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3.3 Stability Criteria in Terms of Two Measures |
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143 | (7) |
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3.4 A Converse Theorem in Terms of Two Measures |
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150 | (6) |
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3.5 Boundedness and Lagrange Stability in Terms of Two Measures |
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156 | (2) |
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3.6 Stability Results for Autonomous or Periodic Systems |
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158 | (4) |
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3.7 Perturbing Family of Lyapunov Functions |
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162 | (8) |
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3.8 M0-Stability Criteria |
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170 | (7) |
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3.9 Several Lyapunov Functions |
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177 | (18) |
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3.9.1 Vector Lyapunov functions method |
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177 | (13) |
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3.9.2 Matrix-valued Lyapunov functions method |
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190 | (5) |
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3.10 Cone Valued Lyapunov Functions |
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195 | (4) |
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199 | (2) |
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4 Stability of Perturbed Motion |
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201 | (52) |
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201 | (1) |
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4.1 Stability of Perturbed Motion in Two Measures |
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202 | (3) |
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4.2 Stability of Perturbed Motion (Continued) |
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205 | (4) |
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4.3 A Technique in Perturbation Theory |
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209 | (7) |
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4.4 Stability of Delay Differential Equations |
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216 | (11) |
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4.5 Stability of Integro-Differential Equations with Finite Memory |
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227 | (4) |
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4.6 Stability of Integro-Differential Equations of Volterra Type |
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231 | (3) |
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4.7 Integro-Differential Equations (Continued) |
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234 | (3) |
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4.8 Stability of Difference Equations |
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237 | (4) |
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4.9 Impulse Differential Equations |
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241 | (8) |
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4.10 Reaction-Diffusion Equations |
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249 | (3) |
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252 | (1) |
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5 Stability in the Models of Real World Phenomena |
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253 | (58) |
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253 | (1) |
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5.1 Stability of a Robot Interacting with a Dynamic Medium |
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254 | (16) |
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5.2 Stabilization of Motions of Affine System |
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270 | (3) |
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5.3 Synchronization of Motions |
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273 | (3) |
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5.4 Stability of Regular Synchronous Generation of Optically Coupled Lasers |
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276 | (9) |
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5.5 Models of World Dynamics and Sustainable Development |
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285 | (8) |
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5.6 Stability Analysis of Impulsive Takagi-Sugeno Systems |
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293 | (15) |
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293 | (11) |
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5.6.2 Impulsive Fuzzy Control for Ecological Prey--Predator Community |
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304 | (4) |
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308 | (3) |
| References |
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311 | (16) |
| Index |
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327 | |
