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| ``...The results presented in Chapter 1 for impulsive differential equations are then applied to an intriguing problem from pharmacokinetics related to intermittent administration of drug dosages…it is a natural problem to be modeled by an impulsive initial value problem for both continuous dependence and stability...'' read more |
| Professor J. Henderson, Baylor University |
| ``...Impulsive differential equations have attracted the interest of many researchers; this monograph will be of interest to researchers currently interested in the field...'' read more |
| Professor Paul W. Eloe, University of Dayton |
Authors
Angel Dishliev1, Katya Dishlieva2, Svetoslav Nenov3| 1,3Postal address: | Department of Mathematics |
| University of Chemical Technology and Metallurgy | |
| 8, Kliment Ohridsky, Sofia, 1756, BULGARIA | |
| 1e-mail: | dishliev@uctm.edu |
| 3e-mail: | svety@math.uctm.edu |
| 2Postal address: | Faculty of Applied Mathematics and Informatics |
| Technical University of Sofia | |
| 8, Kliment Ohridsky, Sofia, 1756, BULGARIA | |
| 2e-mail: | kgd@tu-sofia.bg |
Contents
| Introduction | viii | |
|---|---|---|
| Chapter 1. Continuous Dependence and Stability of the Solutions of Impulsive Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Moments | 1 | |
| 1 | Continuous Dependence of the Solutions of Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Moments | 3 |
| 2 | Stability of the Solutions of Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Moments | 13 |
| 3 | Application: Continuous Dependence and Stability of the Solutions of Pharmacokinetic Model with Fixed Moments of Impulses on the Initial Condition and Impulsive Moments | 23 |
| Chapter 2. Continuous Dependence and Diferentiability of the Solutions of Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 29 | |
| 1 | Continuous Dependence of the Solutions of Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 31 |
| 2 | Differentiability of the Solutions of Differential Equations with Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 37 |
| 3 | Application: Continuous Dependence and Differentiability of the Solutions of Logistic Model with Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 49 |
| Chapter 3. Continuous Dependence and Uniform Stability of the Solutions of the Differential Equations with Variable Moments of Impulses on the Impulsive Hypersurfaces and Impulsive Effects | 53 | |
| 1 | Sufficient Conditions for the Absence of the Phenomenon ``Beating'' | 57 |
| 2 | Continuous Dependence of the Solutions of the Differential Equations with Variable Impulsive Moments on the Impulsive Hypersurfaces | 85 |
| 3 | Uniform Stability of the Solutions of the Differential Equations with Variable Impulsive Moments on the Initial Condition and Impulsive Perturbations | 99 |
| Chapter 4. Continuous Dependence of the Solutions of Differential Equations with Variable Moments of Impulses on the Initial Condition and Barrier Curves | 107 | |
| 1 | Continuous Dependence of the Solutions of Differential Equations with Not Fixed Moments of Impulses on the Initial Condition and Barrier Curves | 109 |
| 2 | Application: Continuous Dependence of the Solutions of the Gompertz Model with Non Fixed Moments of Impulses on the Initial Condition and Barrier Curves | 129 |
| Chapter 5. Orbital Hausdorff Continuous Dependence of the Solutions of Autonomous Differential Equations with Non Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 133 | |
| 1 | Orbital Hausdorff Continuous Dependence of the Solutions of Autonomous Differential Equations with Non Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 135 |
| 2 | Application: Orbital Hausdorff Continuous Dependence of the Solutions of Lotka-Volterra Model with Non Fixed Moments of Impulses on the Initial Condition and Impulsive Effects | 147 |
| Chapter 6. Orbital Hausdorff Stability of the Solutions of Autonomous Differential Equations with Non Fixed Moments of Impulses on the Initial Condition | 157 | |
| 1 | Orbital Hausdorff Stability of the Solutions of Autonomous Differential Equations with Non Fixed Moments of Impulses on the Initial Condition | 159 |
| 2 | Orbital Hausdorff Stability of the Solutions of Lotka-Volterra Model without Impulses on the Initial Condition | 177 |
| 3 | Orbital Hausdorff Stability of the Solutions of Model of Harmonic Oscillator | 189 |
| Chapter 7. Optimization Problems in Population Dynamics | 195 | |
| 1 | Minimization of the Time Required for Reproduction of an Isolated Population | 197 |
| 2 | Application: A Model of Optimal Regime of Outer Effects | 207 |
| 3 | Impulsive Controllability and Optimization Problems. Lagrange's Method | 209 |
| 4 | Application: Impulsive Controllability and Optimization Problems in Population Dynamics | 219 |
| Chapter 8. Continuous Dependence of the Solutions of Differential Equations with Variable Structure and Non Fixed Moments of Impulses with Respect to the Switching Functions | 227 | |
| 1 | Continuous Dependence of the Solutions of the Differential Equations with Variable Structure and Non Fixed Moments of Impulses with Respect to the Switching Functions | 229 |
| 2 | Modelling by the Differential Equations with Variable Structure and Non Fixed Moments of Impulses | 247 |
| Bibliography | 261 | |
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