Planar Schrödinger-Poisson system with steep potential well: supercritical exponential case
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910302827708416 |
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| author | Shen, Liejun Squassina, Marco |
| author_facet | Shen, Liejun Squassina, Marco |
| contents | We study a class of planar Schrödinger-Poisson systems
$$
-Δu+λV(x)u+ϕu=f(u) , \quad x\in{\mathbb R}^2,\qquad
Δϕ=u^2, \quad x\in{\mathbb R}^2, $$ where $λ>0$ is a parameter, $V\in C({\mathbb R}^2,{\mathbb R}^+)$ has a potential well $Ω\triangleq\text{int}\, V^{-1}(0)$ and the nonlinearity $f$ fulfills the supercritical exponential growth at infinity in the Trudinger-Moser sense. By exploiting the mountain-pass theorem and elliptic regular theory, we establish the existence and concentrating behavior of ground state solutions for sufficiently large $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planar Schrödinger-Poisson system with steep potential well: supercritical exponential case Shen, Liejun Squassina, Marco Analysis of PDEs 35J15, 35J20, 35B06 We study a class of planar Schrödinger-Poisson systems $$ -Δu+λV(x)u+ϕu=f(u) , \quad x\in{\mathbb R}^2,\qquad Δϕ=u^2, \quad x\in{\mathbb R}^2, $$ where $λ>0$ is a parameter, $V\in C({\mathbb R}^2,{\mathbb R}^+)$ has a potential well $Ω\triangleq\text{int}\, V^{-1}(0)$ and the nonlinearity $f$ fulfills the supercritical exponential growth at infinity in the Trudinger-Moser sense. By exploiting the mountain-pass theorem and elliptic regular theory, we establish the existence and concentrating behavior of ground state solutions for sufficiently large $λ$. |
| title | Planar Schrödinger-Poisson system with steep potential well: supercritical exponential case |
| topic | Analysis of PDEs 35J15, 35J20, 35B06 |
| url | https://arxiv.org/abs/2401.10663 |