Sub-supersolutions method for singular quasilinear systems involving gradient terms

TL;DR

This paper develops a sub-supersolution method to establish existence and regularity of positive solutions for singular quasilinear elliptic systems with gradient dependence, addressing complex convective and absorption cases.

Contribution

It introduces a new sub-supersolution approach tailored for singular quasilinear systems with gradient terms, expanding the theoretical framework for such problems.

Findings

Proved existence of positive solutions for a class of singular systems.

Established regularity results for solutions.

Applied theorems to systems with convective and absorption singularities.

Abstract

Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are applied to prove the existence of positive solutions for convective and absorption singular systems.