## Differential and Integral Equations

### A Lazer-Mckenna type problem with measures

#### Abstract

In this paper, we are concerned with a general singular Dirichlet boundary value problem whose model is the following: $$\begin{cases} -\Delta u = \frac{\mu}{u^{\gamma}} & \text{in}\ \Omega,\\ u=0 &\text{on}\ \partial\Omega,\\ u>0 &\text{on}\ \Omega\,. \end{cases}$$ Here, $\mu$ is a nonnegative bounded Radon measure on a bounded open set $\Omega\subset\mathbb R^N$, and $\gamma>0$.

#### Article information

Source
Differential Integral Equations, Volume 29, Number 1/2 (2016), 19-36.

Dates
First available in Project Euclid: 24 November 2015