Weak Cyclic Monotonicity and Existence of Solutions of Differential Inclusions

TL;DR

This paper introduces the concept of weak cyclic monotonicity for set-valued maps and proves the existence of solutions to differential inclusions with such right-hand sides in R^n.

Contribution

It generalizes cyclic monotonicity to weak cyclic monotonicity and establishes solution existence for differential inclusions with non-convex, upper semi-continuous right-hand sides.

Findings

Existence of solutions under weak cyclic monotonicity

Extension to non-convex, upper semi-continuous set-valued maps

Generalization of cyclic monotonicity concept

Abstract

The notion of weak cyclic monotonicity of set-valued maps generalizing the cyclic monotonicity is introduced. The existence of solutions of differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n is proved for weakly cyclic monotone right-hand sides.