Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}. By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial no...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-04-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0248 |
| _version_ | 1828155105696808960 |
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| author | Tao Mengfei Zhang Binlin |
| author_facet | Tao Mengfei Zhang Binlin |
| author_sort | Tao Mengfei |
| collection | DOAJ |
| description | In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}. By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the same approach. Finally, we obtain the corresponding existence results for the fractional (p, q)-Laplacian systems in the case of N=sp=lqN=sp=lq. It is worth pointing out that using fixed point argument to seek solutions for a class of nonhomogeneous fractional (p, q)-Laplacian systems is the main novelty of this article. |
| first_indexed | 2024-04-11T22:48:34Z |
| format | Article |
| id | doaj.art-fa88e795342344ec89da9aca0a4d209a |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-11T22:48:34Z |
| publishDate | 2022-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-fa88e795342344ec89da9aca0a4d209a2022-12-22T03:58:39ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2022-04-011111332135110.1515/anona-2022-0248Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearitiesTao Mengfei0Zhang Binlin1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, P. R. ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, P. R. ChinaIn this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}. By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the same approach. Finally, we obtain the corresponding existence results for the fractional (p, q)-Laplacian systems in the case of N=sp=lqN=sp=lq. It is worth pointing out that using fixed point argument to seek solutions for a class of nonhomogeneous fractional (p, q)-Laplacian systems is the main novelty of this article.https://doi.org/10.1515/anona-2022-0248fractional (p, q)-laplacian systemcritical nonlinearitieschoquard nonlinearitiesfixed point theorem35j4735r1147g20 |
| spellingShingle | Tao Mengfei Zhang Binlin Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities Advances in Nonlinear Analysis fractional (p, q)-laplacian system critical nonlinearities choquard nonlinearities fixed point theorem 35j47 35r11 47g20 |
| title | Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities |
| title_full | Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities |
| title_fullStr | Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities |
| title_full_unstemmed | Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities |
| title_short | Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities |
| title_sort | solutions for nonhomogeneous fractional p q laplacian systems with critical nonlinearities |
| topic | fractional (p, q)-laplacian system critical nonlinearities choquard nonlinearities fixed point theorem 35j47 35r11 47g20 |
| url | https://doi.org/10.1515/anona-2022-0248 |
| work_keys_str_mv | AT taomengfei solutionsfornonhomogeneousfractionalpqlaplaciansystemswithcriticalnonlinearities AT zhangbinlin solutionsfornonhomogeneousfractionalpqlaplaciansystemswithcriticalnonlinearities |