Large solutions for the elliptic $1$-Laplacian with absorption

TL;DR

This paper establishes conditions for the existence and uniqueness of large solutions to the elliptic 1-Laplacian equation with absorption, extending classical Keller-Osserman conditions to the case p=1.

Contribution

It introduces a general absorption condition analogous to Keller-Osserman for the 1-Laplacian and provides criteria for solution uniqueness.

Findings

Derived a Keller-Osserman type condition for the 1-Laplacian

Established existence of large solutions under this condition

Provided uniqueness criteria for solutions

Abstract

In this paper we give a general condition on the absorption term of the 1-Laplace elliptic equation for the existence of suitable large solutions. This condition can be considered as the correspondent Keller-Osserman condition for the $p$-Laplacian, in the case $p=1$. We also provide conditions that guarantee uniqueness for solutions to such problems.