Least energy solutions and group invariant solutions of the Hénon equation (Q2866676)
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scientific article; zbMATH DE number 6238502
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Least energy solutions and group invariant solutions of the Hénon equation |
scientific article; zbMATH DE number 6238502 |
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13 December 2013
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Hénon equation
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group invariant solution
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least energy solution
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nonradial positive solution
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variational method
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0.8928921
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0.8883797
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0.88716197
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0.8729763
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0.8693094
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0.86870515
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0.86798507
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0.86438775
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Least energy solutions and group invariant solutions of the Hénon equation (English)
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The Dirichlet problem of the generalized Hénon equation \(-\Delta u(x)=h(|x|) u(x)^p\) in \(B\), \(u=0\) on \(\partial B\) is studied in the unit ball \(B\). The function \(h\) might change sign, but it is supposed that \(h_+ \not \equiv 0\). It is proved that there is a positive solution in \(H^1(B)\) that is not radially symmetric.
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