# American Institute of Mathematical Sciences

September  2010, 9(5): 1335-1343. doi: 10.3934/cpaa.2010.9.1335

## On positive solution to a second order elliptic equation with a singular nonlinearity

 1 Department of Applied Mathematics, Bauman Moscow State Technical University, 2-aya Baumanskaya, 5, 105005 Moscow, Russian Federation

Received  August 2009 Revised  October 2009 Published  May 2019

We consider a second order elliptic equation with measurable bounded coefficients

$(a_{ij}(x)u_{x_i})_{x_j}+p(x)|x|^su^{-\sigma}=0, x\in\Omega \setminus \{ O\},$

where $\sigma >0$, $s$ is any real number, and $\Omega\subset R^n$, $n\ge 3$ is a bounded domain, which contains the origin $O$.
The aim of this paper is to establish existence, nonexistence and behavior of positive weak solutions near the isolated singularity $O$.

Citation: Galina V. Grishina. On positive solution to a second order elliptic equation with a singular nonlinearity. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1335-1343. doi: 10.3934/cpaa.2010.9.1335
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