A generalized porous medium equation related to some singular quasilinear problems

In this paper we study existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is $\begin{cases} -\sum_{m=1}^{\infty} a_m Δu^m= f&\text{in}\ Ω\newline u=0 & \text{on}\ \partialΩ\,, \end{cases}$ where $Ω$ is a bounded domain of $\mathbb{R}^N$, $a_m$ is a sequence of nonnegative real numbers, and $f$ is in $L^q(Ω)$, $q>\frac{N}{2}$.

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