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

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.