Two-point problem for vector differential inclusions with discontinuous right-hand side

Abstract

Given a multifunction , we consider the two-point problemWe prove an existence theorem for solutions , where for each the multifunction can fail to be lower semicontinuous even at all points . Our result extends a previous result, valid for case where and does not depend on .

Keywords:

• differential inclusions
• Riemann-measurable selections
• lower semicontinuity
• null-measure projections

AMS Subject Classifications:

• 34A60
• 54C65
• 28B20

Acknowledgement

The research of J.C. Yao was partially supported by the Grant NSC 102-2115-M-037-002-MY3.