Existence of radial solutions of the Kohn–Laplacian problem

Abstract

The existence of at least one positive radial solution of the generalized Kohn–Laplacian problem (1) −ΔHnu+R(ξ)u=∑i=1kai(|ξ|Hn)|u|pi−2u −∑j=1mbj(|ξ|Hn)|u|qj−2u ξ∈Ω,u>0ξ∈Ω,∂u∂n=0ξ∈∂Ω,(1) is proved, where ΔHn is the Kohn–Laplacian (Heisenberg–Laplacian) operator, Ω is a Korányi ball, ai,1≤i≤k and bj,1≤j≤m are nonnegative radial functions and R(ξ) satisfies some suitable conditions.

Topics & Concepts