Existence results for fractional Brezis-Nirenberg type problems in unbounded domains - Shen, Yansheng; Wang, Xumin (Topological Methods in Nonlinear Analysis, 2022)
In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domains align* cases (-Δ)^su-μu|x|^2s =λ u+|u|^2^*_s-2u & in Ω, u=0 & in R^NΩ, cases align* where (-Δ)^s is the fractional Laplace operator with s(0,1), μ[0,Λ_N,s) with Λ_N,s the best fractional Hardy constant, λ> 0, N> 2s and 2^*_s=2N/(N-2s) denotes the fractional critical Sobolev exponent. By applying the fractional Poincaré inequality together with the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove an existence result to the equation.