Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition
In this paper, we investigate the existence of infinitely many solutions to a fractional p-Kirchhoff-type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: [a+b(∫R2Nux-uypKx-ydxdy)]Lpsu-λ|u|p-2u=gx,u, in Ω, u=0, in RN∖Ω, where Lps is a nonlocal integrodif...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/1353961 |
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| _version_ | 1832555434476568576 |
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| author | Xiangsheng Ren Jiabin Zuo Zhenhua Qiao Lisa Zhu |
| author_facet | Xiangsheng Ren Jiabin Zuo Zhenhua Qiao Lisa Zhu |
| author_sort | Xiangsheng Ren |
| collection | DOAJ |
| description | In this paper, we investigate the existence of infinitely many solutions to a fractional p-Kirchhoff-type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: [a+b(∫R2Nux-uypKx-ydxdy)]Lpsu-λ|u|p-2u=gx,u, in Ω, u=0, in RN∖Ω, where Lps is a nonlocal integrodifferential operator with a singular kernel K. We only consider the non-Ambrosetti-Rabinowitz condition to prove our results by using the symmetric mountain pass theorem. |
| format | Article |
| id | doaj-art-cee0176c2854422fb4b80542a4c4c8f2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-cee0176c2854422fb4b80542a4c4c8f22025-02-03T05:48:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/13539611353961Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) ConditionXiangsheng Ren0Jiabin Zuo1Zhenhua Qiao2Lisa Zhu3College of Science, Hohai University, Nanjing 211100, ChinaCollege of Science, Hohai University, Nanjing 211100, ChinaSchool of Electronic and Information Engineering, Jiangxi Industry Polytechnic College, Nanchang 330099, ChinaSchool of Applied Science, Jilin Engineering Normal University, Changchun 130052, ChinaIn this paper, we investigate the existence of infinitely many solutions to a fractional p-Kirchhoff-type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: [a+b(∫R2Nux-uypKx-ydxdy)]Lpsu-λ|u|p-2u=gx,u, in Ω, u=0, in RN∖Ω, where Lps is a nonlocal integrodifferential operator with a singular kernel K. We only consider the non-Ambrosetti-Rabinowitz condition to prove our results by using the symmetric mountain pass theorem.http://dx.doi.org/10.1155/2019/1353961 |
| spellingShingle | Xiangsheng Ren Jiabin Zuo Zhenhua Qiao Lisa Zhu Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition Advances in Mathematical Physics |
| title | Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition |
| title_full | Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition |
| title_fullStr | Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition |
| title_full_unstemmed | Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition |
| title_short | Infinitely Many Solutions for a Superlinear Fractional p-Kirchhoff-Type Problem without the (AR) Condition |
| title_sort | infinitely many solutions for a superlinear fractional p kirchhoff type problem without the ar condition |
| url | http://dx.doi.org/10.1155/2019/1353961 |
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