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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2305.01705 |
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| _version_ | 1866913616099278848 |
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| author | Sakuma, Masaki |
| author_facet | Sakuma, Masaki |
| contents | We prove the existence of infinitely many solutions to a fractional Choquard type equation \[ (-Δ)^s_p u+V(x)|u|^{p-2}u=(K\ast g(u))g'(u)+\varepsilon_W W(x)f'(u)\quad\text{in }\mathbb{R}^N \] involving fractional $p$-Laplacian and a general convolution term with critical growth. In order to obtain infinitely many solutions, we use a type of the symmetric mountain pass lemma which gives a sequence of critical values converging to zero for even functionals. To assure the $(PS)_c$ conditions, we also use a nonlocal version of the concentration compactness lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01705 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for $p$-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method Sakuma, Masaki Analysis of PDEs We prove the existence of infinitely many solutions to a fractional Choquard type equation \[ (-Δ)^s_p u+V(x)|u|^{p-2}u=(K\ast g(u))g'(u)+\varepsilon_W W(x)f'(u)\quad\text{in }\mathbb{R}^N \] involving fractional $p$-Laplacian and a general convolution term with critical growth. In order to obtain infinitely many solutions, we use a type of the symmetric mountain pass lemma which gives a sequence of critical values converging to zero for even functionals. To assure the $(PS)_c$ conditions, we also use a nonlocal version of the concentration compactness lemma. |
| title | Infinitely many solutions for $p$-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.01705 |