Heisenberg群上无穷远处的集中列紧原理和具有Sobolev临界指数的p - 次Laplace方程多解的存在性

通过建立Heisenberg群上无穷远处的集中列紧原理, 研究了如下$p$ -次Laplace方程 -Δ_{H, p}u=λg(ξ)|u|^q-2u+f (ξ)|u|^p*-2u,在Hⁿ上, u∈ D^{1, p}(Hⁿ), 其中ξ∈Hⁿ,λ∈R,1j, 且m, j为整数.

A Concentration-Compactness Principle at Infinity on the Heisenberg Group and Multiplicity of Solutions for p-sub-Laplacian Problem Involving Critical Sobolev Exponents

The main results of this paper establish the concentration-compactness principle at infinity on the Heisenberg group. The authors consider the p-sub-Laplacian problem involving critical Sobolev exponents   -Δ_{H, p}u=λg(ξ)|u|^q-2u+f (ξ)|u|^p*-2u,  in Hⁿ,  u ∈ D^{1, p}(Hⁿ),  where ξ ∈ Hⁿ, λ ∈ R,1j, both m and j are   integers. The concentration-compactness principle allows  to prove the Palais-Smale condition is satisfied below a certain level.