Elliptic Partial Differential Equation involving singularity

A. Panda, S. Ghosh, D. Choudhuri

Published 2017-09-04Version 1

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