Radial and non-radial solutions of \(-\Delta u=\lambda f(u)\) on an annulus of \(\mathbb{R}^ n\), \(n\geq 3\) (Q1206399)
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scientific article; zbMATH DE number 148861
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Radial and non-radial solutions of \(-\Delta u=\lambda f(u)\) on an annulus of \(\mathbb{R}^ n\), \(n\geq 3\) |
scientific article; zbMATH DE number 148861 |
Statements
Radial and non-radial solutions of \(-\Delta u=\lambda f(u)\) on an annulus of \(\mathbb{R}^ n\), \(n\geq 3\) (English)
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1 April 1993
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The purpose of this paper is to find \(u\in C^{2,\alpha} (\overline {\Omega})\) such that \[ -\Delta u(x)= \lambda e^{u(x)}, \;u(x)>0 \quad \text{in} \quad \Omega, \qquad u(x)=0 \quad \text{on} \quad \partial\Omega, \] when \(\Omega\) is an annulus of \(\mathbb{R}^ n\), \(n\geq 3\).
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Conley index
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symmetry breaking
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