Existence of entire solutions for singular quasilinear convective elliptic systems

TL;DR

This paper proves the existence of entire solutions for a class of singular quasilinear elliptic systems with convective terms, using auxiliary problems, a priori estimates, and fixed point methods.

Contribution

It introduces a novel approach combining auxiliary problem solving and regularization techniques to establish solutions for complex singular systems.

Findings

Existence of weak solutions for the considered elliptic systems.

Development of a regularization-localization procedure.

Application of fixed point arguments to nonlinear problems.

Abstract

The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is first solved. Then, a priori estimates, fixed point arguments, nonlinear regularity, compactness results concerning the gradient terms, besides a regularization-localization procedure, yield the existence of a weak solution to the problem.