Correia, Jeziel N.Oliveira, Claudionei2023-05-152023-05-152022-11-22Correia, J. N., & Oliveira, C. P. (2022). Existence of positive solutions for fractional Laplacian systems with critical growth. <i>Electronic Journal of Differential Equations, 2022</i>(79), pp. 1-42.1072-6691https://hdl.handle.net/10877/16803In this article, we show the existence of positive solution to the nonlocal system (-Δ)s u + α(x)u = 1/2*s Hu(u, v) in ℝN, (-Δ)s v + b(x)v = 1/2*s Hv(u, v) in ℝN, u, v > 0 in ℝN, u, v ∈ Ds,2 (ℝN). We also prove a global compactness result for the associated energy functional similar to that due to Struwe in [26]. The basic tools are some information from a limit system with a(x) = b(x) = 0, a variant of the Lion's principle of concentration and compactness for fractional systems, and Brouwer degree theory.Text42 pages1 file (.pdf)enAttribution 4.0 InternationalFractional LaplacianConcentration-compactnessCritical nonlinearity global compactnessArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.