Existence of Positive Solution of a Class of Semi-linear Sub-elliptic Equation in the Entire Space Hⁿ

الأصل · EN

In this paper, we study the following problem {ll Δₕₙ u-u+uᵖ=0 & in Hⁿ u>0& in Hⁿ u(x)→ 0 &ρ(x)→∞. where 1<p < Q+2/Q-2, Q is the homogeneous dimension of Heisenberg group Hⁿ. Our main result is that this problem has at least one positive solution.