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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World Scientific Publishing
2024-12-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360724500085 |
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| author | Jiaxing An Jingbo Dou Yunyun Hu |
| author_facet | Jiaxing An Jingbo Dou Yunyun Hu |
| author_sort | Jiaxing An |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-96eb47aa8fa44c05aacbfc5e18b50aa6 |
| institution | Kabale University |
| issn | 1664-3607 1664-3615 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj-art-96eb47aa8fa44c05aacbfc5e18b50aa62024-12-20T01:51:17ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152024-12-01140310.1142/S1664360724500085Existence of solutions for the fractional Nirenberg problem with indefinite curvature functionsJiaxing An0Jingbo Dou1Yunyun Hu2School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi, 710119, P. R. ChinaSchool of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi, 710119, P. R. ChinaSchool of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi, 710119, P. R. ChinaIn 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.https://www.worldscientific.com/doi/10.1142/S1664360724500085Fractional Nirenberg problemconformal invariant operatorvariational structuremountain pass lemmablowing-up analysis method |
| spellingShingle | Jiaxing An Jingbo Dou Yunyun Hu Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions Bulletin of Mathematical Sciences Fractional Nirenberg problem conformal invariant operator variational structure mountain pass lemma blowing-up analysis method |
| title | Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions |
| title_full | Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions |
| title_fullStr | Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions |
| title_full_unstemmed | Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions |
| title_short | Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions |
| title_sort | existence of solutions for the fractional nirenberg problem with indefinite curvature functions |
| topic | Fractional Nirenberg problem conformal invariant operator variational structure mountain pass lemma blowing-up analysis method |
| url | https://www.worldscientific.com/doi/10.1142/S1664360724500085 |
| work_keys_str_mv | AT jiaxingan existenceofsolutionsforthefractionalnirenbergproblemwithindefinitecurvaturefunctions AT jingbodou existenceofsolutionsforthefractionalnirenbergproblemwithindefinitecurvaturefunctions AT yunyunhu existenceofsolutionsforthefractionalnirenbergproblemwithindefinitecurvaturefunctions |