Time-Dependent Differential Inclusions and Viability

AMS subject classification: Primary 34A60, Secondary 49J52.

This paper is devoted to study the existence of viable solutions for nonautonomous higher order differential inclusions. Two cases are considered, according to the properties of the set-valued maps on the right-hand side. Firstly, upper semicontinuity is assumed and both necessary and sufficient conditions are given by means of higher order tangent sets. Later, almost upper semicontinuous case is investigated, and similar results are stated. Finally, these results are used to solve a multivalued differential inequality.

This paper was partially supported by DGICYT grant PB95-1103.