Existence solutions for a couple of differential inclusions involving maximal monotone operators

Abstract

In this paper we prove, in a separable Hilbert space, the existence of solutions to a couple of differential inclusions, both of them governed by time and state-dependent maximal monotone operators, and with multi-valued perturbations. An application to an optimal control problem is also presented.

Keywords:

• Absolutely continuous variation
• normal cone
• maximal monotone operator
• multi-valued perturbation
• optimization problem
• pseudo-distance

AMS Subject Classifications: 2020:

• 34A06
• 34K27
• 47B02
• 28C20

Acknowledgments

The authors thank the referee for its valuable remarks and suggestions which helped to improve the last version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).