We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally arises in the study of Ricci solitons structures. We prove existence and nonexistence results, focusing on the radial case, under some general hypothesis on the potential.

中文翻译：

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欧氏空间上具势的共形Yamabe问题

我们考虑在欧几里得环境中，一个与经典常数标量曲率问题的潜在泛化有关的共形Yamabe型方程，该方程自然地出现在Ricci孤子结构的研究中。在一些关于潜能的一般假设下，我们以径向情况为中心证明存在和不存在的结果。