Fractional Sobolev-Choquard critical systems with Hardy term and weighted singularities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| author | Assunção, Ronaldo B. Miyagaki, Olímpio H. Siqueira, Rafaella F. S. |
| author_facet | Assunção, Ronaldo B. Miyagaki, Olímpio H. Siqueira, Rafaella F. S. |
| contents | In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem also includes a homogeneous singular Hardy term; moreover, all the nonlinearities involve singular critical weights. To prove the main result we use a refinement of Sobolev inequality that is related to Morrey space because our problem involves doubly critical exponentss and a version of the Caffarelli-Kohn-Nirenberg inequality. With the help of these results, we provide sufficient conditions under which a weak nontrivial solution to the problem exists via variational methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Sobolev-Choquard critical systems with Hardy term and weighted singularities Assunção, Ronaldo B. Miyagaki, Olímpio H. Siqueira, Rafaella F. S. Analysis of PDEs In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem also includes a homogeneous singular Hardy term; moreover, all the nonlinearities involve singular critical weights. To prove the main result we use a refinement of Sobolev inequality that is related to Morrey space because our problem involves doubly critical exponentss and a version of the Caffarelli-Kohn-Nirenberg inequality. With the help of these results, we provide sufficient conditions under which a weak nontrivial solution to the problem exists via variational methods. |
| title | Fractional Sobolev-Choquard critical systems with Hardy term and weighted singularities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.09650 |