The Dirichlet problem for possibly singular elliptic equations with degenerate coercivity

Abstract

We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla u}{(1+u)^{\theta(p-1)}}\right) = h(u)f \quad \text{in }\Omega, \end{equation*} where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge 2$), $p>1$, $\theta\ge 0$, $f\geq 0$ belongs to a suitable Lebesgue space and $h$ is a continuous, nonnegative function which may blow up at zero and it is bounded at infinity.