Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem (Q949626)

The authors study the problem \[ \begin{cases}\Delta u=u^{-q}+\lambda u^{p},&\text{in }\Omega,\\ u=0, &\text{on }\partial\Omega,\end{cases} \] where \(\Omega\) is a bounded domain in \(\mathbb R^{N}\), \(q>0\), \(p>1\), and \(\lambda>0\), and obtain existence and multiplicity of positive solution.