In this paper we study a class of singular systems with double-phase energy. The main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coefficient. In such a way, we continue the analysis introduced in [6] to the case of lack of compactness corresponding to the whole Euclidean space. After establishing a related compactness property, we establish the existence of solutions for the Baouendi-Grushin singular system.

中文翻译：

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Baouendi-Grushin算子的具有可变增长的奇异双相系统

在本文中，我们研究了一类具有双相能量的奇异系统。主要特征是，相关的Euler方程由具有可变系数的Baouendi-Grushin算符驱动。通过这种方式，我们继续进行[6缺乏对应于整个欧几里德空间的紧凑性的情况。建立相关的紧致性后，我们建立了Baouendi-Grushin奇异系统解的存在性。