On The Extremal Parameters Curve of a Quasilinear Elliptic System of Differential Equations

TL;DR

This paper investigates the extremal parameters of a quasilinear elliptic system with indefinite super-linear nonlinearity, extending results on the existence of positive solutions using the Nehari manifold approach.

Contribution

It introduces an analysis of extremal parameters for a quasilinear elliptic system with indefinite super-linear nonlinearity, expanding the understanding of solution existence.

Findings

Identification of extremal parameters for the system

Extension of existence results for positive solutions

Application of Nehari manifold method

Abstract

We consider a system of quasilinear elliptic equations, with indefinite super-linear nonlinearity, depending on two real parameters $\lambda,\mu$. By using the Nehari manifold and the notion of extremal parameter, we extend some results concerning existence of positive solutions.