Guiding functions and periodic solutions for inclusions with causal multioperators

Abstract

In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered. Thereafter, the theory is extended to the case of non-smooth guiding functions.

Keywords:

• Periodic solution
• differential inclusion
• causal operator
• guiding function

AMS Subject Classifications:

• Primary: 34C25
• Secondary: 34A60
• 34K09

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the first and the second authors was supported by the RFBR [grant number 14-01-00468]; RSF [grant number 14-21-00066]. The work of the third author was supported by the Università di Firenze research grant and the work of the second author was partially supported by INdAM.