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Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq1$, let$K$, $M$ be two nonnegative functions and let $\alpha,\gamma>0$. We studyexistence and nonexistence of positive solutions for singular problems of theform $-\Delta u=K\left( x\right) u^{-\alpha}-\lambda M\left( x\right)u^{-\gamma}$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\lambda>0$ is areal parameter. We mention that as a particular case our results apply toproblems of the form $-\Delta u=m\left( x\right) u^{-\gamma}$ in $\Omega$,$u=0$ on $\partial\Omega$, where $m$ is allowed to change sign in $\Omega$.

On Dirichlet problems with singular nonlinearity of indefinite sign