Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents

TL;DR

This paper establishes existence and bounds for positive solutions of singular quasilinear elliptic systems with variable exponents using Schauder's fixed point theorem and Moser iteration.

Contribution

It introduces new methods for proving existence and boundedness of solutions in variable exponent elliptic systems with singularities.

Findings

Proved existence of positive solutions

Derived a priori estimates and boundedness

Applied Schauder's fixed point theorem and Moser iteration

Abstract

This article sets forth results on the existence, a priori estimates and boundedness of positive solutions of a singular quasilinear systems of elliptic equations involving variable exponents. The approach is based on Schauder's fixed point Theorem. A Moser iteration procedure is also obtained for singular cooperative systems involving variable exponents establishing a priori estimates and boundedness of solutions.