Positive solutions with prescribed mass for a planar Choquard equation with critical growth
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918000253206528 |
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| author | Huang, Ling Romani, Giulio |
| author_facet | Huang, Ling Romani, Giulio |
| contents | We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of a positive radial solution by a variational argument, which exploits a delicate analysis on the mountain pass level. Under an additional monotonicity assumption on the nonlinearity, such a solution turns out to be also a ground state in $H^1(\mathbb R^2)$. Our work extends the results by Dou, Huang, and Zhong (J Geom Anal 34(10):317, 2024) to the Choquard setting, improving in several directions those by Deng and Yu in (Z Angew Math Phys 74(3):103, 2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive solutions with prescribed mass for a planar Choquard equation with critical growth Huang, Ling Romani, Giulio Analysis of PDEs 35J20, 35J91, 35Q55, 35R09, 35B33 We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of a positive radial solution by a variational argument, which exploits a delicate analysis on the mountain pass level. Under an additional monotonicity assumption on the nonlinearity, such a solution turns out to be also a ground state in $H^1(\mathbb R^2)$. Our work extends the results by Dou, Huang, and Zhong (J Geom Anal 34(10):317, 2024) to the Choquard setting, improving in several directions those by Deng and Yu in (Z Angew Math Phys 74(3):103, 2023). |
| title | Positive solutions with prescribed mass for a planar Choquard equation with critical growth |
| topic | Analysis of PDEs 35J20, 35J91, 35Q55, 35R09, 35B33 |
| url | https://arxiv.org/abs/2407.20618 |