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

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

2002-12-20

arxiv.org/abs/math/0212283v1

Mathematics

Analysis of PDEs

14pages, no fingures

Scientific paper

In this paper, we study the following problem $$ \{{ll} \Delta_{H^n}
u-u+u^p=0 & in H^n u>0& in H^n u(x)\to 0 &\rho(x)\to\infty}. $$ where $1

\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.

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