On Variational Inequalities with Multivalued Operators with Semi-Bounded Variation

TL;DR

This paper investigates the solvability of steady-state variational inequalities involving multivalued operators, focusing on the properties of radially semi-continuous operators with semi-bounded variation and their relation to monotonicity.

Contribution

It introduces new insights into the connections between semi-bounded variation operators and classes of pseudo-monotone and monotone mappings.

Findings

Established conditions for solvability of variational inequalities.

Characterized properties of radially semi-continuous operators with semi-bounded variation.

Linked these operators to pseudo-monotone and monotone mappings.

Abstract

In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and classes of pseudo-monotone and monotone mappings, and some properties of this operators.