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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… Click to show full abstract
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 $O$.
Keywords:
elliptic equation;
positive solution;
order elliptic;
second order
Journal Title: Communications on Pure and Applied Analysis
Year Published: 2019
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Journal Title: Communications on Pure and Applied Analysis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!