Positive solutions for infinite semipositone/positone quasilinear elliptic systems with singular and superlinear terms

TL;DR

This paper proves the existence and regularity of positive solutions for complex quasilinear elliptic systems with singular and superlinear terms, using sub-supersolution methods and Schauder's fixed point theorem.

Contribution

It introduces a novel approach combining sub-supersolution techniques with fixed point theory to handle singular and superlinear terms in elliptic systems.

Findings

Established existence of positive solutions

Proved regularity of solutions

Applied fixed point methods to complex systems

Abstract

We establish existence and regularity of positive solutions for a class of quasilinear elliptic systems with singular and superlinear terms. The approach is based on sub-supersolution methods for systems of quasilinear singular equations and the Schauder's fixed point Theorem.