by V Lakshmikantham (Florida Inst. of Technology), D D Bainov (Plovdiv Univ.), & P S Simeonov (Plovdiv Univ.)

Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.

• Description of Systems with Impulses
• Existence and Continuation
• Pulse Phenomena
• Impulsive Differential Inequalities
• Impulsive Integral Inequalities
• Global Existence
• Dependence on Initial Values
• Differentiability Relative to Initial Values
• Method of Upper and Lower Solutions
• Monotone Iterative Technique
• Stability by Linear Approximation
• Vector Lyapunov Functions
• Stability Concepts in Terms of Two Measures
• Quasistability Criteria
• Singularly Perturbed Systems
• Systems with Variable Structure
• Integro-Differential Systems
• Periodic Boundary Value Problems for Second Order Systems