Singular quasilinear convective elliptic systems in $R^N$

TL;DR

This paper proves the existence of positive solutions for a class of singular quasilinear elliptic systems with convection terms in Euclidean space, using advanced mathematical techniques to ensure solutions are strong and regular.

Contribution

It introduces new existence results for singular quasilinear elliptic systems with convection, employing perturbation, fixed point, and regularity methods.

Findings

Existence of positive weak solutions established.

Solutions are shown to be strong and regular.

Methodology combines perturbation, fixed point, and a priori estimates.

Abstract

The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity results are then employed to show that the obtained solution is actually strong.