Non-instantaneous impulsive differential equations : basic theory and computation
Impulsive differential equations
IOP Publishing
2018
EISBN 9780750317047
1. Linear and perturbed equations.
1.1. Stability analysis.
1.2. Lyapunov regularity
2. Nonlinear differential equations.
2.1. Continuous dependence and stability of solutions.
2.2. Orbital Hausdorff dependence of the solutions.
2.3. Differentiability of solutions
3. Semilinear evolution equations.
3.1. First-order evolution equations.
3.2. Second-order evolution equations
4. Periodic solutions.
4.1. First-order autonomous evolution equations.
4.2. First-order non-autonomous evolution equations.
4.3. Second-order evolution equations.
Many real-life processes can be characterised by rapid changes in their state. Some of these changes begin impulsively and are not negligible. For changes such as these, mathematical models called non-instantaneous differential equations are created. These models give rise to a new, hybrid dynamical system that can be used for many different purposes. Using a variety of equations, examples and solutions, this book will be an essential guide for researchers, graduate students and those interested in applied mathematics and related fields.
1.1. Stability analysis.
1.2. Lyapunov regularity
2. Nonlinear differential equations.
2.1. Continuous dependence and stability of solutions.
2.2. Orbital Hausdorff dependence of the solutions.
2.3. Differentiability of solutions
3. Semilinear evolution equations.
3.1. First-order evolution equations.
3.2. Second-order evolution equations
4. Periodic solutions.
4.1. First-order autonomous evolution equations.
4.2. First-order non-autonomous evolution equations.
4.3. Second-order evolution equations.
Many real-life processes can be characterised by rapid changes in their state. Some of these changes begin impulsively and are not negligible. For changes such as these, mathematical models called non-instantaneous differential equations are created. These models give rise to a new, hybrid dynamical system that can be used for many different purposes. Using a variety of equations, examples and solutions, this book will be an essential guide for researchers, graduate students and those interested in applied mathematics and related fields.
