The homogeneous Hénon-Lane-Emden system (Q745917)

In the interesting paper under review, the authors employ variational methods to study the existence of a principal eigenvalue for the homogeneous Hénon-Lane-Emden system \[ \begin{cases} -\Delta u=\lambda_1| x|^a| v|^{p'-2}v & \text{in }\Omega,\\ -\Delta v=\lambda_2 | x|^b| u|^{p-2}u & \text{in }\Omega,\\ u=v=0 & \text{on }\partial\Omega,\end{cases} \] where \(\Omega\subset\mathbb R^n\), \(n\geq 1\) is a bounded domain containing the origin, \(a\), \(b>-n\), and \(p\), \(p'=\frac{p}{p-1}\in(1,\infty)\) satisfy \[ \dfrac{a}{p'}+\dfrac{b}{p}+2>0. \] A detailed insight into the problem in the linear case \(p=2\) is provided as well.