On large ring solutions for Gierer–Meinhardt system in R3R3

We consider the stationary radial solution in the classical Gierer–Meinhardt system in R3R3:{ϵ2Δu−u+u2v=0in R3,Δv−v+u2=0in R3,u,v>0,u(x),v(x)→0as |x|→+∞. We prove the existence of a large ring-like solution. This complements an earlier work of Ni and Wei (2006) [30] in which the existence of O(1)O(1) ring solutions was proved in R2R2.