The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity. (Q454531)
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scientific article; zbMATH DE number 6092256
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity. |
scientific article; zbMATH DE number 6092256 |
Statements
The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity. (English)
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8 October 2012
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elliptic Kirchhoff equation
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ground-state solution
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Berestycki-Lions assumptions
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The author proves the existence of a positive solution on \(C^2(\mathbb {R}^N)\) to the equation NEWLINE\[NEWLINE -M(\int _{\mathbb {R}^N}| \nabla u| ^2)\Delta u=g(u) NEWLINE\]NEWLINE in \(\mathbb {R}^N\), (\(N\geq 3\)) for zero-mass Berestycki-Lions nonlinearity. In the second part of the paper the existence of a ground-state solution of the above equation with \(M(s)=a+bs\), \(g(u)\) being a zero-mass Berestycki-Lions nonlinearity and \(N=3,4\), is studied.
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