This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space \(\mathbb {R}^N_+\) \((N\ge 3)\) satisfying nonlinear boundary conditions for \(1<p<N\). Moreover, the symmetry of positive solutions is shown by using the method of moving planes.

中文翻译：

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上半空间中的 $$p-$$ 调和函数

本文研究上半空间 \ (\mathbb {R}^N_+\) \((N\ge 3)\)中 p 调和函数的存在、不存在和定性性质，满足非线性边界条件为\ (1<p<N\)。而且，利用移动平面的方法来证明正解的对称性。