Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities
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| Format: | Preprint |
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2024
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| _version_ | 1866909338909540352 |
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| author | Assunção, Ronaldo Brasileiro Miyagaki, Olímpio Hiroshi Siqueira, Rafaella Ferreira dos Santos |
| author_facet | Assunção, Ronaldo Brasileiro Miyagaki, Olímpio Hiroshi Siqueira, Rafaella Ferreira dos Santos |
| contents | In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes a Hardy-type term; additionaly, all terms have critical singular weights. Our result improve upon previous work in the following ways: we focus our attention on the existence of a nontrivial weak solution for fractional p-Kirchhoff equation in the entire space R^N. The possibility of a slower growth in the nonlinearity makes it more difficult to establish a compactness condition; to do so, we use the Cerami condition. The crucial points in our argument are the uniform boundedness of the convolution part and the lack of compactness of the Sobolev embeddings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_05185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities Assunção, Ronaldo Brasileiro Miyagaki, Olímpio Hiroshi Siqueira, Rafaella Ferreira dos Santos Analysis of PDEs In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes a Hardy-type term; additionaly, all terms have critical singular weights. Our result improve upon previous work in the following ways: we focus our attention on the existence of a nontrivial weak solution for fractional p-Kirchhoff equation in the entire space R^N. The possibility of a slower growth in the nonlinearity makes it more difficult to establish a compactness condition; to do so, we use the Cerami condition. The crucial points in our argument are the uniform boundedness of the convolution part and the lack of compactness of the Sobolev embeddings. |
| title | Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.05185 |