A generalized porous medium equation related to some singular quasilinear problems

Abstract

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

References in corpus (1)

• Quasilinear elliptic equations with singular quadratic growth terms