Asymptotics for Semilinear Elliptic Systems
Ezzat S. Noussair, Charles A. Swanson · Canadian Mathematical Bulletin · 1991
Abstract A class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞. Additional results concern the existence and structure of positive solutions u with finite energy in a neighbourhood of infinity.