Abstract
The theory of impulsive di'erential equations is emerging as an important area of investigation since it is richer in problems in comparison with the corresponding theory of di'erential equations and many of the mathematical problems encountered in studying the impulsive di'erential equations cannot be treated with the usual techniques of ordinary di'erential equations [7,9,11]. Moreover, impulsive di'erential systems represent a natural framework for mathematical modelling of several processes in natural science. That is why in recent years the study of such systems has been very intensive. However, the theory of integro-di'erential equations with impulse actions on surfaces has not yet been su9ciently elaborated when compared to that of impulsive di'erential equations and integro-di'erential equations. There are also several problems on the controllability problem for impulsive systems which are connected with the results of the theory of integral and integro-di'erential equations and have not been well investigated yet [5,6,8,10].
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