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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66052In 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 dimension of Heisenberg group $H^n$. Our main result is that this problem has at least one positive solution.14pages, no finguresAnalysis of PDEsDifferential Geometry35J60Existence of Positive Solution of a Class of Semi-linear Sub-elliptic Equation in the Entire Space $H^n$text