Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions
In this paper, we investigate the following fractional Nirenberg problem: Pσg𝕊n(u) = c(n,σ)Rσḡ(x)un+2σ n−2σon𝕊n, where [Formula: see text] is fractional order conformal invariant operator and [Formula: see text] is the [Formula: see text]-curvature for [Formula: see text] with [Formula: see text] wi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2024-12-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360724500085 |
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| Summary: | In this paper, we investigate the following fractional Nirenberg problem: Pσg𝕊n(u) = c(n,σ)Rσḡ(x)un+2σ n−2σon𝕊n, where [Formula: see text] is fractional order conformal invariant operator and [Formula: see text] is the [Formula: see text]-curvature for [Formula: see text] with [Formula: see text] with [Formula: see text] and [Formula: see text]. We show the existence results to the above equation employing the variational method and blowing-up analysis method, when the rotationally symmetric and indefinite curvature function [Formula: see text] satisfies certain flatness conditions. |
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| ISSN: | 1664-3607 1664-3615 |