Here, the existence of at least one positive radial solution of the Nonlinear nonhomogeneous Neumann problem $-{\mathrm{\Delta }}_{{\mathbb{H}}^n}u+R\left(\xi \right)u=a\left(|\xi {|}_{{\mathbb{H}}^n}\right)\frac{|u{|}^{q-2}u}{1+|u{|}^{q-p}}-b\left(|\xi {|}_{{\mathbb{H}}^n}\right)|u{|}^{q-2}u,\xi \in \mathrm{\Omega }$ is proved on the Heisenberg group ${\mathbb{H}}^n$, via variational principle, where Ω is the Korányi ball, a and b are nonnegative radial functions and $R\left(\xi \right)$ holds in some suitable conditions.

中文翻译：

---

Heisenberg 群上的非线性非齐次 Neumann 问题

这里，非线性非齐次 Neumann 问题的至少一个正径向解的存在$-{\mathrm{\Delta }}_{{\mathbb{H}}^n}你+R\left(\xi \right)你=\mathrm{一种}\left(|\xi {|}_{{\mathbb{H}}^n}\right)\frac{|你{|}^{q-2}你}{1+|你{|}^{q-p}}-b\left(|\xi {|}_{{\mathbb{H}}^n}\right)|你{|}^{q-2}你,\xi \in \mathrm{\Omega }$在海森堡群上证明${\mathbb{H}}^n$，通过变分原理，其中 Ω 是 Korányi 球，a和b是非负径向函数，并且$R\left(\xi \right)$在一些合适的条件下成立。