On continuous variations of trajectories of differential inclusion with unbounded right-hand side

ABSTRACT

The property of the continuous dependence of the trajectories of the differential inclusion with a measurable pseudo-Lipschitz unbounded right-hand side on the initial approximations in Euclidean space is proved. This property is an important part of the direct method of obtaining the necessary optimality conditions in the extremal problems with constraints in the form of a differential inclusion.

KEYWORDS:

• Multivalued mapping
• differential inclusion
• derivative of the multivalued mapping
• Clarke tangent cone
• measurable pseudo-Lipschitz mapping

AMS CLASSIFICATIONS:

• 34A60
• 49J21
• 49K21

Acknowledgments

The author is grateful to the anonymous referee for his/her valuable suggestions and remarks that allowed me to improve the original presentation.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Russian Foundation for Basic Research (project nos. 18-01-00209a).