| Summary: | We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $−\Delta u +\frac{|\nabla u|^2}}{u^\gamma} = f$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is an open bounded subset of $\mathbb{R}$, $\gamma > 0$ and $f$ is a function which is strictly positive on every compactly contained subset of $\Omega$. As a consequence of our main results, we prove that the condition $\gamma<2$ is necessary and sufficient for the existence of solutions in $H^1_0(\Omega)$ for every sufficiently regular $f$ as above.
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