# Regularizing effect of absorption terms in singular problems

@article{Oliva2019RegularizingEO, title={Regularizing effect of absorption terms in singular problems}, author={Francescantonio Oliva}, journal={Journal of Mathematical Analysis and Applications}, year={2019} }

We prove existence of solutions to problems whose model is
$$\begin{cases}
\displaystyle -\Delta_p u + u^q = \frac{f}{u^\gamma} & \text{in}\ \Omega, \newline
u\ge0 &\text{in}\ \Omega,\newline
u=0 &\text{on}\ \partial\Omega,
\end{cases}$$
where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge2$), $\Delta_p u$ is the $p$-laplacian operator for $1\le p 0$, $\gamma\ge 0$ and $f$ is a nonnegative function in $L^m(\Omega)$ for some $m\ge1$. In particular we analyze the regularizing…

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