High and low perturbations of the critical Choquard equation on the Heisenberg group

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2023-10-20 DOI:10.57262/ade029-0304-153

Shujie Bai, Yueqiang Song, Duvsan D. Repovvs

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引用次数: 0

Abstract

We study the following critical Choquard equation on the Heisenberg group: \begin{equation*} \begin{cases} \displaystyle {-\Delta_H u }={\mu} |u|^{q-2}u+\int_{\Omega} \frac{|u(\eta)|^{Q_{\lambda}^{\ast}}} {|\eta^{-1}\xi|^{\lambda}} d\eta|u|^{Q_{\lambda}^{\ast}-2}u&\mbox{in }\ \Omega, u=0&\mbox{on }\ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset \mathbb{H}^N$ is a smooth bounded domain, $\Delta_H$ is the Kohn-Laplacian on the Heisenberg group $\mathbb{H}^N$, $10$, $0<\lambda

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海森堡群上临界乔卡方程的高扰动和低扰动

我们研究海森堡群上的下列临界乔夸尔方程：\Begin{equation*}\开始\{-Delta_H u }={mu} |u|^{q-2}u+\int_{\Omega} \frac{|u(\eta)|^{Q_{\lambda}^{\ast}} }{|\eta^{-1}\xi|^{\lambda}} d\eta|u|^{Q_{\lambda}^{\ast}-2}u&\mbox{in }\Omega, u=0&\mbox{on }\partial\Omega, （end{cases｝\end{equation*} 其中 $\Omega\subset \mathbb{H}^N$ 是光滑有界域，$\Delta_H$ 是海森堡群 $\mathbb{H}^N$ 上的 Kohn-Laplacian, $10$, $0<\lambda

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.

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