Multiple solutions to Bahri-Coron problem involving fractional p-Laplacian in some domain with nontrivial topology - Kumar, Uttam; Tiwari, Sweta (Topological Methods in Nonlinear Analysis, 2023)
In this article, we establish the existence of positive and multiple sign-changing solutions to the fractional p-Laplacian equation with purely critical nonlinearity equation Ppomegas-aP_p,Ω^s cases (-Δ)_p^s u =|u|^p_s^*-2 u& in Ω, u =0 & on Ω^c, cases equation in a bounded domain ΩR^N for s(0,1), p(1,∞), and the fractional critical Sobolev exponent p^*_s=Np/(N-sp) under some symmetry assumptions. We study Struwe’s type global compactness results for the Palais-Smale sequence in the presence of symmetries.