Existence and Nonexistence Results for Classes of Singular Elliptic Problem

Abstract

The singular semilinear elliptic problem $-\Delta u+k\left(x\right)u^{-\gamma }=\lambda u^p$ in $\Omega$, $u>0$ in $\Omega$, $u=0$ on $\partial \Omega$, is considered, where $\Omega$ is a bounded domain with smooth boundary in $R^N$, $k\in C_{\text{loc}}^{\alpha }\left(\Omega \right)\cap C\left(\overline{\Omega }\right)$, 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.