On the Two-Dimensional Gierer--Meinhardt System with Strong Coupling
Juncheng Wei, Matthias Winter · SIAM Journal on Mathematical Analysis · 1999
We construct solutions with a single interior condensation point for the two-dimensional Gierer--Meinhardt system with strong coupling. The condensation point is located at a nondegenerate critical point of the diagonal part of the regular part of Green's function for $ -\Delta +1 $ under the Neumann boundary condition. Our method is based on the Liapunov--Schmidt reduction for a system of elliptic equations.