Normalized Solutions for Schrödinger-Bopp-Podolsky Systems with Critical Choquard-Type Nonlinearity on Bounded Domains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915706791002112 |
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| author | Chen, Li Wang, Li |
| author_facet | Chen, Li Wang, Li |
| contents | In this paper, we study normalized solutions for the following critical Schrödinger-Bopp-Podolsky system: $$-Δu + q(x)ϕu = λu + |u|^{p-2}u + \bigl(I_α* |u|^{3+α}\bigr)|u|^{1+α}u,\quad \text{in } Ω_r,$$ $$-Δϕ+ Δ^2ϕ= q(x)u^2, \ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\ \text{ in } Ω_r,$$ where $Ω_r \subset \mathbb R^3$ is a smooth bounded domain, $p \in \left(2, \frac{8}{3}\right)$, $q(x) \in C(\barΩ_r) \backslash \{0\}$ and $λ\in \mathbb R$ is the Lagrange multiplier associated with the constraint $\int_{Ω_r} |u|^2\, \mathrm d x = b^2$ for some $b > 0$. Here $α> 0$, $I_α$ denotes the Riesz potential, and the domain parameter $r$ reflects the size of $Ω_r$ whose precise definition will be given in Section 3. By applying a special minimax principle together with a truncation technique, we prove that there exists $b^* > 0$ such that the system admits multiple normalized solutions whenever $b \in (0, b^*)$ under Navier boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01098 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normalized Solutions for Schrödinger-Bopp-Podolsky Systems with Critical Choquard-Type Nonlinearity on Bounded Domains Chen, Li Wang, Li Analysis of PDEs 35J60, 35J50, 35B38, 35J20 In this paper, we study normalized solutions for the following critical Schrödinger-Bopp-Podolsky system: $$-Δu + q(x)ϕu = λu + |u|^{p-2}u + \bigl(I_α* |u|^{3+α}\bigr)|u|^{1+α}u,\quad \text{in } Ω_r,$$ $$-Δϕ+ Δ^2ϕ= q(x)u^2, \ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\ \text{ in } Ω_r,$$ where $Ω_r \subset \mathbb R^3$ is a smooth bounded domain, $p \in \left(2, \frac{8}{3}\right)$, $q(x) \in C(\barΩ_r) \backslash \{0\}$ and $λ\in \mathbb R$ is the Lagrange multiplier associated with the constraint $\int_{Ω_r} |u|^2\, \mathrm d x = b^2$ for some $b > 0$. Here $α> 0$, $I_α$ denotes the Riesz potential, and the domain parameter $r$ reflects the size of $Ω_r$ whose precise definition will be given in Section 3. By applying a special minimax principle together with a truncation technique, we prove that there exists $b^* > 0$ such that the system admits multiple normalized solutions whenever $b \in (0, b^*)$ under Navier boundary conditions. |
| title | Normalized Solutions for Schrödinger-Bopp-Podolsky Systems with Critical Choquard-Type Nonlinearity on Bounded Domains |
| topic | Analysis of PDEs 35J60, 35J50, 35B38, 35J20 |
| url | https://arxiv.org/abs/2601.01098 |