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Significant interest in the investigation of systems with
discontinuous trajectories is explained by the development of
equipment in which significant role is played by impulsive control
systems and impulsive computing systems. Impulsive systems are also
encountered in numerous problems of natural sciences described by
mathematical models with conditions reflecting the impulsive action
of external forces with pulses whose duration can be neglected.
Differential equations with set-valued right-hand side arise in the
investigation of evolution processes in the case of measurement
errors, inaccuracy or incompleteness of information, action of
bounded perturbations, violation of unique solvability conditions,
etc. Differential inclusions also allow one to describe the
dynamics of controlled processes and are widely used in the theory
of optimal control. This monograph is devoted to the investigation
of impulsive differential equations with set-valued and
discontinuous right-hand sides. It is intended for researchers,
lecturers, postgraduate students, and students of higher schools
specialized in the field of the theory of differential equations,
the theory of optimal control, and their applications.
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