In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.

中文翻译：

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海森堡群上带有非线性源的p-次拉普拉斯算子的解的存在性

在本文中，我们证明了在Heisenberg群上具有Dirichlet边界条件的非线性p -sub-Laplacian方程的弱解的存在。在证明中，我们使用了山峰定理和Folland-Stein嵌入定理作为主要工具。