Singular quasilinear elliptic systems with (super-) homogeneous conditions

TL;DR

This paper investigates the existence, nonexistence, and regularity of positive solutions for singular quasilinear elliptic systems under homogeneous conditions, using sub-supersolution and perturbation methods.

Contribution

It introduces a novel approach combining sub-supersolution techniques with perturbation arguments to analyze singular quasilinear elliptic systems.

Findings

Established conditions for existence of positive solutions

Identified scenarios leading to nonexistence of solutions

Proved regularity results for solutions

Abstract

In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for systems of quasilinear singular equations combined with perturbation arguments involving singular terms.