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Article Contents

# Asymptotic behavior for the unique positive solution to a singular elliptic problem

• In this paper, by means of sub-supersolution method, we are concerned with the exact asymptotic behavior for the unique solution near the boundary to the following singular Dirichlet problem $-\triangle u=b(x)g(u), u>0, x \in \Omega, u|_{\partial \Omega}=0$, where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$, $b \in C^{\alpha}_{l o c}({\Omega})$ ($0 < \alpha < 1$), is positive in $\Omega,$ may be vanishing or singular on the boundary, $g\in C^1((0,\infty), (0,\infty))$, $g$ is decreasing on $(0,\infty)$ with $\lim\limits_{s \rightarrow 0^+}g(s)=\infty$ and satisfies some appropriate assumptions related to Karamata regular variation theory.
Mathematics Subject Classification: Primary: 35J25, 35B40; Secondary: 35J67.

 Citation:

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