multi-function differential inclusion directional continuity upper and low semi-continuity measurability Department of Operations Research
Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
An existence theorem is proved for solutions of differential inclusions with an upper semicontinuous and nonconvex right-hand side. The proof is based on an inner and directional continuous parameterization. This parameterization leads to a familie of disturbed differential inclusions. The solution of the starting differential inclusion is obtained as an uniformly limit of the solutions of disturbed systems. Some aspects of the existence of the above mentioned inner parameterization are discussed. A few examples are presented.
AMS (MOS) subject classification: 34A60.