A new result on the existence and non-existence of positive solutions for two-parametric systems of quasilinear elliptic equations

TL;DR

This paper investigates conditions under which positive solutions exist or do not exist for a two-parameter quasilinear elliptic system involving the $(p,q)$-Laplacian, extending previous results with new methods.

Contribution

It introduces new existence and non-existence results for positive solutions of a two-parameter $(p,q)$-Laplacian system with indefinite nonlinearity, using an adapted sub-supersolution approach.

Findings

Established new conditions for positive solutions existence.

Identified parameter ranges where solutions do not exist.

Extended previous theoretical results with novel methods.

Abstract

This paper is devoted to the existence and non-existence of positive solutions for a $(p, q)$-Laplacian system with indefinite nonlinearity depending on two parameters $(\lambda,\mu)$. By using the sub-supersolution method together with adaptations of ideas found in \cite{AAS,CRMZ}, we extend some previous result.