带有部分调和位势以及临界增长的 Schrödinger-Poisson 系统基态解的存在性——献给邓引斌教授 70 寿辰

Abstract

Abstract:

In this paper, the following Schrödinger-Poisson system with partial confinement and critical growth

$\begin{eqnarray*} \begin{cases} -\Delta u+(x_1^2+x_2^2)u+\phi u=\vert u\vert^{p-2}u+\vert u\vert^{4}u, & x\in \mathbb{R}^3,\\ -\Delta \phi =u^{2}, & x\in \mathbb{R}^3, \end{cases} \end{eqnarray*}$

is studied, where $p\in (4,6)$. By using variational method, we prove the existence of a positive ground state solution. Moreover, via energy comparison, we also prove the nonexistence of least-energy sign-changing solution.

Key words: Schr?dinger-Poisson system, partial confinement, critical growth, ground state solution

CLC Number:

O175.25

Liying Shan, Wei Shuai, Ping Yang, Jianghua Ye. Existence of Ground State Solution for Schrödinger-Poisson System with Partial Confinement and Critical Growth[J].Acta mathematica scientia,Series A, 2026, 46(4): 1529-1547.

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References 38

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Existence of Ground State Solution for Schrödinger-Poisson System with Partial Confinement and Critical Growth

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