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Article Contents

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

• 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 $O$.

Mathematics Subject Classification: Primary: 35J15, 35J61, 35J75; Secondary: 35A01, 35Bxx.

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