Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent
Abstract In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions. Also, we prove some further properties of solutions.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1239-4 |
| _version_ | 1819025781521645568 |
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| author | Jichao Wang Jian Zhang Yujun Cui |
| author_facet | Jichao Wang Jian Zhang Yujun Cui |
| author_sort | Jichao Wang |
| collection | DOAJ |
| description | Abstract In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions. Also, we prove some further properties of solutions. |
| first_indexed | 2024-12-21T05:16:08Z |
| format | Article |
| id | doaj.art-c1b1ac6ce4c7497ea0eabbfdb1a44ea2 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-21T05:16:08Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-c1b1ac6ce4c7497ea0eabbfdb1a44ea22022-12-21T19:14:55ZengSpringerOpenBoundary Value Problems1687-27702019-07-012019111710.1186/s13661-019-1239-4Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponentJichao Wang0Jian Zhang1Yujun Cui2College of Science, China University of PetroleumCollege of Science, China University of PetroleumDepartment of Mathematics, Shandong University of Science and TechnologyAbstract In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions. Also, we prove some further properties of solutions.http://link.springer.com/article/10.1186/s13661-019-1239-4Fractional equationKirchhoff typeHardy–Littlewood–Sobolev critical exponentMultiple solution |
| spellingShingle | Jichao Wang Jian Zhang Yujun Cui Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent Boundary Value Problems Fractional equation Kirchhoff type Hardy–Littlewood–Sobolev critical exponent Multiple solution |
| title | Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent |
| title_full | Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent |
| title_fullStr | Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent |
| title_full_unstemmed | Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent |
| title_short | Multiple solutions to the Kirchhoff fractional equation involving Hardy–Littlewood–Sobolev critical exponent |
| title_sort | multiple solutions to the kirchhoff fractional equation involving hardy littlewood sobolev critical exponent |
| topic | Fractional equation Kirchhoff type Hardy–Littlewood–Sobolev critical exponent Multiple solution |
| url | http://link.springer.com/article/10.1186/s13661-019-1239-4 |
| work_keys_str_mv | AT jichaowang multiplesolutionstothekirchhofffractionalequationinvolvinghardylittlewoodsobolevcriticalexponent AT jianzhang multiplesolutionstothekirchhofffractionalequationinvolvinghardylittlewoodsobolevcriticalexponent AT yujuncui multiplesolutionstothekirchhofffractionalequationinvolvinghardylittlewoodsobolevcriticalexponent |