Existence of Positive Solution of a Class of Semi-linear Sub-elliptic Equation in the Entire Space $H^n$

Zhu-Jun Zheng, Xiu-Fang Feng

In this paper, we study the following problem $$ \{{ll} Δ_{H^n} u-u+u^p=0 & in H^n u>0& in H^n u(x)\to 0 &ρ(x)\to\infty}. $$ where $1<p<\frac{Q+2}{Q-2}$, Q is the homogeneous dim…