Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up (Q2750855)
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scientific article; zbMATH DE number 1663100
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up |
scientific article; zbMATH DE number 1663100 |
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Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up (English)
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21 October 2001
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sub- and super-solutions
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distance function
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mean curvature
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The paper deals with uniqueness of positive solutions to the problem \(-\Delta u=\lambda(x)u-a(x)u^p,\) \(u|_{\partial\Omega}=+\infty,\) \(p>1,\) \(a(x)>0\) in \(\Omega\) and \(a|_{\partial\Omega}=0.\) Exact asymptotic estimates are provided describing the blow-up rate near \(\partial\Omega\) in terms of the distance function \(\text{dist }(x,\partial\Omega)\) and the mean curvature H of \(\partial\Omega.\)
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