Impulsive Differential Equations

The following sections are included:

• Preface

• Contents

The following sections are included:

• Description of mathematical model

• Systems with impulses at fixed times

• Systems with impulses at variable times

• Discontinuous dynamical systems

• Motion of an impulsive oscillator under the effect of an impulsive force

The following sections are included:

• General properties of solutions of linear systems

• Linear systems with constant coefficients

• Stability of solutions of linear impulsive systems

• Characteristic exponents of functions and matrices of functions

• Adjoint systems. Perron theorem

• Reducible systems

• Linear periodic impulsive systems

• Linear Hamiltonian systems of impulsive differential equations

• Periodic solutions of a certain second order equation

The following sections are included:

• Linear systems with constant and almost constant matrices

• Stability criterion based on first order approximation

• Stability in systems with variable times of impulsive effect

• Direct Lyapunov method for studying stability of solutions of impulsive systems

The following sections are included:

• Nonhomogeneous linear periodic systems

• Nonlinear periodic systems

• Numerical-Analytical method for finding periodic solutions

• Almost periodic sequences

• Almost periodic functions

• Almost periodic differential systems

• Homogeneous linear periodic systems

The following sections are included:

• Bounded solutions of nonhomogeneous linear systems

• Existence of bounded solutions of nonlinear systems

• Integral sets of systems with hyperbolic linear part

• Integral sets of a certain class of discontinuous dynamical systems

The following sections are included:

• Formulation of the problem. Auxiliary results.

• Necessary conditions for optimum

• Impulsive control with fixed times

• Necessary and sufficient conditions for optimum

The following sections are included:

• Formulation of the problem

• Formulas for an approximate solution of a non-resonance system

• Substantiation of the averaging method for a non-resonance system

• Averaging in a resonance system and its substantiation

• Formulas for approximate solutions for an impulsive effect occuring at fixed positions

• Substantiation of the averaging method for systems with impulses occurring at fixed positions

• General averaging scheme for impulsive systems

• On correspondence between exact and approximate solutions over an infinite time interval

The following sections are included:

• Impulsive systems with generally distributed impulses at fixed times

• Periodic impulsive systems with impulses located on a surface

• Unbounded functions with almost periodic differences

• Spaces of almost periodic functions on the line

• Spaces of piecewise continuous almost periodic functions

• Almost periodic measures on the line

• Almost periodic solutions of impulsive ordinary differential equations

• Linear abstract impulsive systems and their almost periodic solutions

• Bibliographical notes

The following sections are included:

• Bibliography

• Subject Index