Singular Quasilinear Elliptic Systems With Gradient Dependence

TL;DR

This paper establishes the existence and regularity of positive solutions for a class of singular quasilinear elliptic systems that include gradient-dependent terms, using comparison principles, a priori estimates, and fixed point theory.

Contribution

It introduces new methods to prove existence and regularity for singular quasilinear elliptic systems with gradient dependence, expanding the theoretical understanding of such systems.

Findings

Proved existence of positive solutions

Established regularity results

Applied Schauder's fixed point theorem

Abstract

In this paper, we prove existence and regularity of positive solutions for singular quasilinear elliptic systems involving gradient terms. Our approach is based on comparison properties, a priori estimates and Schauder's fixed point theorem.