In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star-shaped domain. At last, we extend the results of Pohozaev-type inequalities to elliptic systems, which are used to derive the nonexistence of positive solutions of this type of systems in the non-star-shaped domains. On this basis, we also discuss the existence of positive solutions of a kind of elliptic systems with double critical growth.

中文翻译：

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一类椭圆方程（系统）的Pohozaev型不等式及其应用

在本文中，我们首先在更一般的非星形区域中推导p-Laplacian方程的一种新的Pohozaev型不等式，然后我们用两个例子及其图形来解释这种新形状。非星状区域。最后，我们将Pohozaev型不等式的结果扩展到椭圆系统，该系统用于导出非星形域中此类系统的正解的不存在。在此基础上，我们还讨论了一类具有双重临界增长的椭圆系统的正解的存在性。