Elliptic Partial Differential Equation Involving a Singularity and a Radon measure

Abstract

The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure $\mu$ as its nonhomogenous term which is given as \begin{eqnarray} -Δu&=& f(x)h(u)+μ~\text{in}~Ω,\nonumber u&=&0~\text{on}~\partialΩ,\nonumber u&>& 0~\text{on}~Ω\nonumber, \end{eqnarray} where $\Omega$ is a bounded domain of ${\mathbb{R}}^N$, $f$ is a nonnegative function over $\Omega$.

21 Pages