Abstract
In this paper, we study the existence of nontrivial solutions tothe critical fractional elliptic system on the Heisenberg group:$$\begin{gathered}\begin{cases}(-\Delta_{\mathbb{H}^{n}})^{s} u+\gamma u=\lambda f(\xi)|u|^{r-2} u+\frac{2 \alpha}{\alpha+\beta}|u|^{\alpha-2} u|v|^{\beta} & \text { in } \Omega, \\(-\Delta_{\mathbb{H}^{n}})^{s} v+\nu v=\mu g(\xi)|v|^{r-2} v+\frac{2 \beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2} v & \text { in } \Omega, \\u = v =0 & \text { in } \mathbb{H}^{n}\setminus \Omega,\end{cases}\end{gathered}$$where ${\Delta_{\mathbb{H}^{n}}}$ is the Kohn-Laplacian, $s\in(0,1)$, $ Q > 2 s$ and $\Omega\subset\mathbb{H}^{n}$ is a boundeddomain with smooth boundary. $\lambda, \mu,\gamma,\nu$ are positive real parameters and $ Q=2n+2$ is the homogeneousdimension of ${\mathbb{H}^{n}}$. The exponent $r$ satisfies$1 < r < 2^{*}_{s}$, $\alpha > 1, \beta > 1$ satisfy$2 < \alpha+\beta=2_{s}^{*}$, $2_{s}^{*}= 2Q/(Q-2s)$ being thefractional critical Sobolev exponent. The results presented hereextend or complete recent papers and are new to critical fractionalelliptic system on Heisenberg group.
Citation
Shiqi Li. Yueqiang Song. Mingzhe Sun. "Existence results for a class of critical fractional elliptic system on Heisenberg group." Differential Integral Equations 37 (1/2) 121 - 144, January/February 2024. https://doi.org/10.57262/die037-0102-121
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