impulsive differential system impulsive boundary value problem Cauchy problem Stiеltjеs integral Caratheodory conditions Department of Operations Research
Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
This work considers Impulsive differential systems with boundary conditions. The characteristic feature of the impulsive boundary value problems is the unknown impulse moment. The solvability of the differential systems without impulses does not imply solution for the corresponding impulsive problem. Another specialty of the impulsive boundary value problem is that the set of solutions may not be a closed set.
The problem is considered as a special logically controlled impulsive boundary value problem.
The control may choose to use an optional impulse on the surface S. It is proved that the set of solution of the above mentioned controlled problem with a fixed and finite number of impulses is a closed set. If the boundary conditions describe a compact set then the set of impulsive solutions is a compact set too. The sufficient conditions for the existence of solutions of single impulse linear boundary value problem are presented. An example is considered.
AMS (MOS) subject classification: 34A6O.
[Ivanov R. P.; Иванов Р. П.]; [Kitanov P. M.; Китанов П. М.]