Classification of Stable Solutions to a Non-Local Gelfand–Liouville Equation. (8th September 2020) - Hyder, Ali; Yang, Wen
Abstract: We study finite Morse index solutions to the non-local Gelfand–Liouville problem align*& (-Δ)^su=e^uinR^n, align* for every s(0, 1) and n>2s . Precisely, we prove non-existence of finite Morse index solutions whenever the singular solution align* &u_n, s(x)=-2s|x|+(2^2sΓ(n2)Γ(1+s)Γ(n-2s2))align* is unstable.