Infinitely many nonradial solutions for the Hénon equation with critical growth (Q373508)
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scientific article; zbMATH DE number 6216026
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinitely many nonradial solutions for the Hénon equation with critical growth |
scientific article; zbMATH DE number 6216026 |
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Infinitely many nonradial solutions for the Hénon equation with critical growth (English)
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17 October 2013
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This paper is concerned with qualitative aspects of the Hénon equation \(\star\) with critical growth. Let \(\alpha\) denote the coefficient of \(| y|\) in \(\star\) and \(N\geq 4\) the dimension. First it is shown that for any \(\alpha >0\) there is a nonradial solution. Then, it is shown that \(\star\) has infinitely many nonradial solutions, with arbitrarily large energy. Green functions and contraction maps are used in the proofs.
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Hénon's equation
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infinitely many solutions
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critical Sobolev exponent
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reduction method
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