Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian (Q2871267)
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scientific article; zbMATH DE number 6249046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian |
scientific article; zbMATH DE number 6249046 |
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22 January 2014
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nonlinear problems
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fractional Laplacian
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fractional Sobolev spaces
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critical Sobolev exponent
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spherical solutions
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ground states
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math.AP
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Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian (English)
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In this paper, the authors establish the existence of a radially symmetric solution \(u \in H^s(\mathbb R^N)\) of NEWLINE\[NEWLINE (- \Delta)^s u + u = |u|^{p-1}u NEWLINE\]NEWLINE where \(s\in (0,1)\), \((- \Delta)^s\) is a fractional Laplacian, \(N>2s\) and \(p\in (1, (N+2s)/(N-2s)\).
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