On the absence of solutions of differential inequalities with $\infty$-Laplacian

TL;DR

This paper establishes conditions under which solutions do not exist for certain differential inequalities involving the $ abla$-Laplacian in unbounded domains, supported by illustrative examples.

Contribution

It provides new criteria for the non-existence of solutions to $ abla$-Laplacian inequalities in unbounded regions, enhancing understanding of these equations.

Findings

Conditions for absence of solutions are derived.

Examples confirm the sharpness of the criteria.

Abstract

For differential inequalities with the $\infty$-Laplacian in the principal part, we obtain conditions for the absence of solutions in unbounded domains. Examples are given to demonstrate the accuracy of these conditions.