# 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}
}
• Francescantonio Oliva
• Published 31 October 2018
• Mathematics
• Journal of Mathematical Analysis and Applications
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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