Nonsmooth integral guiding potentials and asymptotic behaviour of solutions for inclusions with causal multioperators

Abstract

In the present paper, differential inclusions with a causal multioperator are considered. We apply the method of nonsmooth integral guiding potentials to the study of the problem on the asymptotic behaviour of solutions for such inclusions. We investigate both the case of a closed and convex-valued right-hand part and the case of a nonconvex-valued and lower semicontinuous right-hand part.

Keywords:

• Differential inclusion
• causal multioperator
• asymptotic behaviour of solutions
• integral guiding potential

2010 Mathematics Subject:

• 34A60
• 34C37
• 34K09
• 34K25

Acknowledgments

The work on the paper was carried out during Prof. V. Obukhovskii's and Prof. S. Kornev's visit to the Center for Fundamental Science, Kaohsiung Medical University and the Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan in 2018. They would like to express their gratitude to the members of the Center and the Department for their kind hospitality. The authors would like to express our deep gratitude to the reviewers for helpful and important comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the first and the second authors is supported by the Ministry of Science and Higher Education of the Russian Federation in the frameworks of the project part of the state work quota (Project No. 1.3464.2017/4.6) and the Taiwan MOST – Russian FBR (Project No. 17-51-52022), the work of the first author is also supported by the Ministry of Science and Higher Education of the Russian Federation (grant number 14.Z50.31.0037), the work of the third author is supported by the Grant MOST 106-2923-E-039-001-MY3.