Existence and nonexistence results for classes of singular elliptic problem (Q1957581)

Summary: The singular semilinear elliptic problem \(-\Delta u+k(x)u^{-\gamma}= \lambda u^p\) in \(\Omega\), \(u>0\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), is considered, where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb R^N\), \(k\in C_{\text{loc}}^a(\Omega)\cap C(\overline{\Omega})\), and \(\gamma,p,\lambda\) are three positive constants. Some existence or nonexistence results are obtained for solutions of this problem by the sub-supersolution method.