Multiple solutions for Schr{ö}dinger-Poisson-Slater equations with critical growth
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913919983943680 |
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| author | Liu, Shibo |
| author_facet | Liu, Shibo |
| contents | We obtain multiple solutions for the zero mass Schr{ö}dinger-Poisson-Slater equation \[ - Δu + \left( \frac{1}{4 π| x |} \ast u^2 \right) u = λg (x) | u |^{p - 2} u + | u |^{6 - 2} u \text{, \ \ \ \ } u \in \mathcal{D}^{1, 2} (\mathbb{R}^3) \text{} \] for $λ\gg 1$, where $p \in (4, 6)$ and $g \in L^{6 / (6 - p)} (\mathbb{R}^3)$. The crucial (PS)$_c$ condition is verified using a simpler method. Similar multiplicity result is also obtained for related equation with an external potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple solutions for Schr{ö}dinger-Poisson-Slater equations with critical growth Liu, Shibo Analysis of PDEs 35J91, 35J20, 47J30 We obtain multiple solutions for the zero mass Schr{ö}dinger-Poisson-Slater equation \[ - Δu + \left( \frac{1}{4 π| x |} \ast u^2 \right) u = λg (x) | u |^{p - 2} u + | u |^{6 - 2} u \text{, \ \ \ \ } u \in \mathcal{D}^{1, 2} (\mathbb{R}^3) \text{} \] for $λ\gg 1$, where $p \in (4, 6)$ and $g \in L^{6 / (6 - p)} (\mathbb{R}^3)$. The crucial (PS)$_c$ condition is verified using a simpler method. Similar multiplicity result is also obtained for related equation with an external potential. |
| title | Multiple solutions for Schr{ö}dinger-Poisson-Slater equations with critical growth |
| topic | Analysis of PDEs 35J91, 35J20, 47J30 |
| url | https://arxiv.org/abs/2507.00295 |